X/ll-Commerce FREE PAST PAPERS Scaned by: f ©) » @CommerceWalyUstaad Part ease ected PON ge Tee Ie eI eae Yd ea ed adPAST PAPERS XII(C) 195 =» STATISTICS STATISTIC 2021 (AS PER CONDENSED SYLLABUS) TIME: 2 Hours (30 Viarks) NOTE: i) This section consists of 25 part questions and all are to be answered. Each question carries ONE marks. ii) Do not copy the part questions in your answer book. Write only the answer in full against the proper number of the question and its part. iii) The‘use of calculator is allowed. _ SECTION ‘A’ (Multiple Choice Questions (25) 1. Choose the correct answer for each from the given options: (i) A die is rolled once, the total sample points will be: *6V *12 *36 *2 (ii) Range is calculated as: * Max. value — Min. value ¥ * Min. value - Max. value * Mean - Mode * Median - Mean (iii) The color of eyes represents: * Quantative data * Qualitative data¥ * Discrete data : * Continuous data (iv) In tossing two coins together the total possible outcomes are: *2 Wv *6 “16 (v) Mean of the data 1,4,2,3,5 is: 5) *10 *15 Ww (vi) §P2 is equal to: *10 *20v *120 *70 (vii) First had information is called: * Mode * Secondary Data ular diagram of data is called: * Multiple bar diagram * Bar diagram (ix) The part of the population under study is called: neter * Sample¥ * Mean * Statistic equal tu: * * Infinity Ww *10 (xi) The median of the data 1, -1, 0, 2, -2 is: “6 *0v "2 *42 mmetrical distribution Mean, Median and Mode are: * Greater than Zero * Equal to Zero formation collected from magazine is:PAST PAPERS XII(C) _—-186. das STATISTICS * Primary data * Continuous datav * Secondary datay” * Discrete data ow S people out of 7 can be selected in: | * 10 ways * Sways * $0 ways * 21 waysY” A | (xv) The graph of frequency distribution . * Bar diagram * Frequency curve v/ | * Pie-diagramy” * Ogive Novi) The probability always lies between: £*3to 10 * Oto lv *-1to +1 *1to 10 (xvii) Fisher Index Number is given by: * VLAP v *VL-P *VL+P WK (xviii) A characteristic of population is called: ~ Mean * Mode * Median * ParameterY (xix) Statistics deals with: » Theory * Graph * Data * Mean (xx) If P(A) = 0.6, P(B) = 0.8, P(A) B) = 0.84 then P(A U B) equal to: + 0.25 + 0.48 * 0.56¥ * 1.40 (xxi) The most repeated value in data is called: * Modev * Mean * Median * Constant (xxii) Median can be located b} * Bar diagram * Histogram — * Pie-Diagram * * Ogivey (xxiii) Mode can be located by: * Histogram¥ * Bar di * Ogive * Pie-diagram (xxiv) If ¥(x— A) = 0. then Arithmetic Mean will be: - 20 *x *x=0 * (xxv) The sum of relative frequencies must be equal toz *3 *2 *lv as NOTE: Attempt any equal marks. 2. i) Draw a Pie diagram for the following table: Ttems Expenditure 2 900 600el PAST PAPERS XII(C) 187 ie» STATISTICS 2. ji) The average wage of 4 men per hour and the rworage wage of Ifa fair is tossed three times: a) What is probability of getting 3 Heads? b) What is the probability of getting 2 Heads? 2. iv) The pice of a Contpddity for 6 years is giver in the following table, (Year | 2015 | 2016 ms [Price 20 [20 23 a Calculate index number a) Taking 2015 as base year b) Using Chain bave method. é . 2. v) Show that the sum of the deviations from their mean is Zero: 13, 7.0 3.6, 4.1, 5.0. SECTION “C” (Detailed Answer Questions) 10) NOTE: Attempt any ONE part questions. All questions carries , equal marks, | 3. Find Mean, Median and Mode of the following frequency distribution and comment on the results: Daily Wages No. of Employees _] +6 2 | 68 5 | 8-10 10 10-12 12-14. 3 | 1-16 1 4. From the following data using 2019 as base year, find: i) Laspyere’s Index Number ii) Paasche’s Index Number iii) Fisher Ideal Index Number Commodities Price I Quantity 2019 2020 «| 2019 2020 mon 64 75 | (270 ~~ ~«2290 EB B 38 6s | (ASS 200 7 c 18 ma [| Bo | Bt j D 30 oO | IM WSSe Ul PAST PAPERS XII(C)__188 Slew STATISTICS — v- STATISTICS 2019 . Time: 15 minutes (Regular & Private) Max. Marks: 10 i) This section consists of 10 part questions and all are to be i answered, Each question carries | mark. . 1 (ii) Do not copy the part questions in your answer script. Write only the answer in full against the proper number of the questions and its part. (iii) Write the code of your question paper in bold letters in the beginning of the answer script. (iv) The use of calculator is allowed. SECTION *A* (MULTIPLE CHOICE QUESTIONS) 1, Choose the correct answer for each from the given options: { () If ¥ = 10 and y = 3z. the y is:* 30 *Rv = *10 | | | (ii)Value index number is equal to: Page LPedn Tred IPod : (iii) The limit of probability is: *-lto+1 *OtolY *1to2 *-2to-1 (iv) Iftwo dice are rolled once, then the probability of getting the same number is: *1/5 *12 * 1/6 *0 (s) The data obtained from the Federal Bureau of Statistics is called: *Secondary Data” *Primary Data » Continuous Data *Complex Data (vi) The median of the data 4.6.3.2.0.1,7 is: *4 *Bv *0 *2 (vii) If the mean of the data of 25 values is 20, then Sx is =: 41 *10 *50 *500V iit) 1f P(A) = 2,P(8/,) = 2 then (An B) =: (viii) If a= 3 i /a) = 70" en P (AN B) = I (és) The number of different arrangements of four persons to sit around 1 table is: “4 *6Y 1G #26 (x) If D(x — A) = 0, then: *AX A=0 +A=%Y STATISTICS 2019 i Al TIME: I Hours 45 Minutes (Regular & Private) (40 Marks) SECTION ‘B’ (SHORT ANSWER — QUESTION) (25 Marks) NO’ Attempt FIVE Part-Questions from this Section. All qu carry equal mark: 2. (i) Different (a) Diserete and etween the follow ‘ontinuous variable.PAST PAPERS XII (C) 189 jtew STATISTICS (b) Primary and Secondary data 2. (iii) In how many ways can the letters of the following words be arranged? (a)TOMORROW (b) YESTERDAY 2. (iv) The following table shows the prices of an items for 5 years. Calculate the index number for all years, taking an average of 1990 and 1991 as base year, (Year, [1990 [1991 11992 [1993 | 1994 1995 1996 | 1997 \ [Price [45 | 50 | 60 | 65 | 70 72 | 8 | ® 2. (v) The probability that Jawwad will pass the test 2/3 and that for Daniyal is 3/4 . Find the probability that (a) Both will pass the test(b) Both will not pass the test 2. (vi) How many three digit numbers can be formed from the digits 1,4,5,7,8,9 if the digits are: (a) repeated —_(b) not repeated 2 The mean of ten numbers is8. If the eleventh number is included in the data, the mean becomes 9. What is the value of the eleventh number? 2. (viii) The following data refers to the prices of rice in a city: 125_ [126 | 135_[ 132_| 130 ps [123 [122] 31] 120 130 [135 [121 | Rs | 126 132 [134135137 [132 138 [129 | 130 [ 124 | 126 $ ‘equency table with call interval of 4 rupees each such that the Prepared lower el Attempt TWO Questions from this Section. All Questions equal marks. late the price index numbers for the following data by applying: COMMODITIES PRICE QUANTITY 2008 | 2009 2008 | 2009 man a et 40 30 | B 3 3 sof 100he Ses PASTPAPERS XII(C) 1903+ STATISTICS { 50 Cc Ls 17 50 Hand the made for the flowing frequency 4. Find the mean, the medi distribution: Class interval 57 8-10 Frequency 2 8 n 3. A bag contains 3 white balls, 4 black balls and 5 red balls. [f 3 balls are drawn at random, find the probability that: (i) All three balls are red (ii) Two balls are red and one ball is black ) all three balls are different colour. STATISTICS 2018 Time: 15 minutes (Regular & Private) Max. Marks: 10 SECTION ¢ IULTIPLE CHOICE QUESTIONS 1. Choose the correct answer for each from the given options: i) The characteristic of population is called: ~ average * statistic * parameterY * variable ii) The sum of deviations measured from its mean is always: * minimum * zero * one * maximum (iii) The number of arrangements of the letters of the word TYPE is: *4 *6 * dv *30 (iv) The graph of cumulative frequency distribution is called: * OgiveY * Histogram * Polygon * Simple Bar diagram (¥) In Paasche's weighted index number, weight is * Base year price * Base year quantity * Current year price * Current year quantity” (vi) Two events, which cannot occur together, are called: * Joint events * Composite events * Mutually exclusive events” * Not mutually exclusive events (vii) If P(A) = 0.4, then P(A): * 04 *0.2 * 0.64 *0. (viii) For the data 5, 8, 10, 6, 10, 12, 15, 10, 6, mode is: *6 *15 *10v *20 | (ix) If two fair coins are tossed, then the probability of getting one tail i 0.50% * 0.70 ait (x) The arithmetic mean of four values is 25, then, x is: *25 * 50 * 80 *100Y |PASTPAPERS XII(C) _191 jew STATISTICS STATISTICS 2018 TIME: | Hours 45 Minutes (Regular & Private) (40 Marks) SECTION ‘B’ (SHORT ANSWER — QUESTION) (25 Marks) NOTE: Attempt any Five questions from this section. All questions carry equal marks, The use of calculator is allowed 2.i) Differentiate between primary and secondary data, and give at least two sources of each kind. ii) Complete the following table: CL [Frequency | Relative Frequency | Cumulative frequency 15 2 2 f 2 6-10 21 2 2 11-15 2 038 I 65 16-20 19 0.19 | 4 21-25 | 16 2 l z _ _ iii) Draw histogram and Frequency polygon for the following frequency distribution: Class Interval | 2-3 | +5 | 67 | &9 [10-11 ) Frequency 1 3 ‘Seo eee iy) For the data 101, 102, 103, 104, 105 and y = x - 100, Find ¥ and ¥ ‘The mean height of 45 students of a class is 60" and the mean height of student of other class is 57". Find the combined mean. Two fair dice are thrown together. Find the probabili points on the top of both dice is 9 or 10. vii) In how many ways can the word UNIVERSITY be arranged? viii) Let A and B are two events in sample space such that P(A) = P(B) = and P(AUB) = : Find P(A n B) SECTION ‘C’ (DETAILED-ANSWER QUESTIONS )(15) NOTE: Attempt any TWO questions from this section. AU questions carry equal marks. The use of calculator is allowed. 3. The following table is about marks awarded to 30 students: (23 [32 [36 [41 [to [25 [41 4315 [34 (17 [5 for 16 [8 [15 [46 [45 39 (33 12 [32 [18 [31 [24 [28 [33 127 134 [os | a) Construct frequency distribution table, making cla nd so on. ¢ cumulative frequency and Relative frequency for the above data. alculate the median, the mode and locate both graphically for the —-—~ following data. y that the sum of 6-10, 11 -PAST PAPERS Xil (C) 192 _Ses STATISTICS { Age (years) O8—12 | 12-16 | 16-20 | 20-24 | 24-28 | Total | Number of 10 1 | 32 17 07 84 [Policy Holders 5. Calculate Laspeyre’s, Paache’s and Fisher's index numbers by taking 1990_as base year. 1990 i 1995 Commodity ~ Price | Quantity | Price | Quantity A 2 | 8 | 2 26 B 25 30 26 25 Cc 24 MOUS 30 D 20 3 | 33 STATISTICS 2017 Time: 15 minutes (Regular & Private) Max. Marks: 10 SECTION ‘A’ (MULTIPLE CHOICE QUESTIONS) 1. Choose the correct answer for each from the given options: i) The median of the data 3,1, -2, 4. 2, 6 is: *2 * 25v *3 * 2 ii)If P(A) = 0.60, P(B) = 0.80 and P(A B) = 0.84, then P(AUB)is: — * -0.20* 1.40 * 0.560 * 0.48 iii) The data obtained from trade journals and magazines is called: * Primary data * Continous data * Discrete data * Secondary data” iv) The age of college students is an example of: * Quantitative variableY * Qualitative variable * Parametric variable * Exogenous variable v) An ogive is drawn to find the: * MedianY * Mode * Index Number * Mean vi) Ifx= 50and y = 3x — 10, then the mean of yis : * 140v * 100 * -10 * —20 vii) The sum of the angles of a pie diagram is equal to: * 180°V * 90° * 360° * 100° viii) A coin is tossed. The probability of getting tail is: * 0.75 * 0.50P - 0.50 1 square root of the product of Laspeyre's and Paashce's ix) The posi index numbers * Price Index Number * Quantity Index Number * Fisher's Index Number * Marshall Index Number x) Two events that cannot happen together are called: * Joint events * Composite eventsPAST PAPERS XII (C) 193 ide» STATISTICS + * Independent events * Mutually exclusive events“ STATISTICS 2017 TIME: | Hours 45 Minutes (Regular & Private) (40 Marks) SECTION ‘B" ORT ANSWER STION Marks, Attempt any Five questions from this section. All questions carry equal marks. The use of calculator is allowed 2.i) Differentiate between the following. (a) Quantitative variable and Qualitative variable (b) Primary data and Secondary data ii) The following data represents the prices of a commodity 125 | 126 | 135 | 132 | 130 128 [123 | 122 | 131_| 130 120 [135 | 121 | 128 | 126 | 132_| 134 | 135 | 137 | 132 138 [129 [130 | 124 | 126 Prepare a frequency distribution taking an interval of size S. Also find Class boundaries and Mid points. ‘Af iii) The mean of 10 numbers is 8. If the eleventh number is included in the T~ data, the mean becomes 9, What is the eleventh number? iv) How many permutations can be made from the letters of the following words? : (a) MILLENIUM (b) ACCOUNTANCY \ev) How many two digit numbers can be formed from the digits 4,5,6,7.8, if * the digits are: (a) repeated? —_(b) not repeated? vi) Following table shows the road accidents in the district East for December 2008. Draw a Pie Chart in your answer script. Type of | Motor Cycles | Buses | Cars [Trucks | Other vehicles ft ‘ No. of 38° 10 1s 18 2 Accidents ! vii) The given table shows the Price of commodities for 6 years. Construct the link relatives: Years | 2000 | 2001 | 2002 | 2003 | 2004 | 2006 Price(Rs.) | 45 [ 52 | 58 | 64 | 72 | 22 }) Three coins are tossed together: da) The sample space b) The probability of getting at most 1 tail. c) The probability of getting at least 2 tails.— . . .: °° °»«. PAST PAPERS XII (C) 194 sien STATISTICS carry equal marks. The use of calculator is allowed. 3. The measurements of the heights of the students of a college are given in the fallowing frequency distribution. (Height | 135-144 | 145-154 | 155-104 | 105-174 | 175-184 | 185-194 [Noof | 5 | 1g 25 32 16 8 [Students _ Find the mean, Median and Mode 4. Calculate a) peyre's Price Index number. sche’s Price Index number. Ideal Index aumber. for the given data taking 2010 as base year. 2010 2011 ‘Commodity Price Quantity Price | Quantity { A 10 iB | 12 16 | | B ma 20 ~{ ~20 22 [ce [25 10 | 30 15 5. Two balanced dice are rolled together. Find the: 2) Sample space b) Probability that the sum of dots on the top faces of both the dice is 11. c) Probability of getting the same number of dots on the top faces of both the dice. STATISTICS 2016 Time: 15 minutes (Regular & Private) Max. Marks: 10 SECTION ‘A’ (MULTIPLE CHOICE QUESTIONS) 1. Choose the correct answer for each from the given options: (i) Ifa card is drawn from a pack of playing cards, then the probability of getting a face card is: * 4/52 *13/52 *1/52 (ii) The blood group of the students of *Quantitative variable *Q *Continuous ble *Discrete v (iii) The number of days in the month of Decem) *Variable *Constant ¥ *Sample *Parameter (iv) If, in a moderately skewed dis mode is: *10 ‘ (v) The mode of the d sav 45 ibution, mean = 35, median = 30, then Ov ‘ *65 a 1,7, 2,3, 4, 5,5, 754, 4, *7 *No mode m this section. All questionsOOS ee PAST PAPERS Xil (C) 195 dew STATISTICS (vi) If Laspeyre's index number ~ 132.5%, Paasche’s index number = 135.75%, then Fisher's index number is: 1% 44.11% *134.11% % *164.11% ra certain distribution, if (x - 15) = Sand S (x - 18) = 0, then mean “0 “15 “a = IFewo fair coins are tossed, then the probability af one head ss: * 0.25 0.500 * 0.75 ef (ix) Data obtained from daily newspaper is called: “Primary “Secondary ¥ * continuous \7(x) If ¥ = SO and y = 3x — 10, then mean of y is: \ *140V *0 “100 STATISTICS 2016 TIME: 1 Hours 45 Minutes (Regular & Private) (40 Marks) SECTION ‘B’ (SHORT ANSWER — QUESTION) (25 Marks. x Attempt any Five part questions from this Section. All questions carry equal marks. 2.i) Describe the sources of the collection of primary data. ii) Draw a pie diagram in your answerscript of the following data. Category | A { B | C | D | E | F | Frequency 9 2 | s7_ | 24 | 10 | 8 | iii) From the given data, calculate price index numbers, taking 1967 as base year using simple Aggregative method. | “none of these *200 Price | |_1967 1970 1973) A I 12.00 15.00 15.60 | “B | 3.00 3.60 3.60 i Cc 15.00 6.00 9.70 } iv) The ages of employees in a department are classified as: [Age in years 16-20 | 21-25 | 26-30 | 31-35 | 36-40 Number ofemployees | 14 2 30 25 4 Draw a histogram and find the mode graphically: vy) The data given below shows the daily wages paid to the workers in a factory. Classify this data taking a class interval of 18 and starting with 100. Also calculate relative frequencies. 240 [16s [175 [iss [210 | 117 | 100 F 140 [175 | 16s | 103 | 14s | 179 _~| 104 ‘ 176_[ 179 [214 | 126 | 147_| 169 [175 : 210Es| 8207s 22528] e278 | e222 et 20 7ee| 17D vos [4s [175 | 107 [172 | 124 [134PAST PAPERS XII 196 Joey STATISTICS Lass [as7 [tes] 179 [tas] 7s] 156] i s~ vi) For a set of 15 observations, the mean came out to be 12, Later on checking it is discovered that an observation 20 was incorrectly recorded whereas the correct value was 02. Calculate the correct mean, ‘A card is drawn from a deck of 52 playing cards. What is the probability that it is: a) Diamond? b) Face card? ii) How many permutations can be formed from the word ‘COMMITTEE’? SECTION ‘C’ (DETAILED-ANSWER QUESTIONS )(15) NOTE: Attempt any TWO questions from this section. All questions carry equal marks. The use of calculator is allowed... 3. Calculate the mean, median and mode of the following data: Group _ | 0-10 [| 10-20 [| 20-30 | 30-40 | 40-50 | 50-60 frequency | 12 | 18 27 "| 20 17 06 4.a) A fair coin is tossed three times what is the probability of getting at least one head? b) What is the probability of getting a total of 7 or 11 when a pair of dice is tossed? c) The probability that a student will pass in Accounting is 6/9 and the probability that he will pass in Statistics Is 8/13, what is the probability that he will pass in both the subjects? 5.a) A bag contains 3 red, 4 white and 3 green balls. If a sample of 3 balls is selected at random, find the probability that: (i) All are of different colours. (ii) Two are of white colour. 5. b) The probability that A will be alive for 30 years is 0.4 and probability that B will be alive for 30 years is 0.8. What is the probability that both will be alive for 30 years? STATISTICS 2015 Time: 15 minutes (Regular & Private) Max. Marks: 10 SECTION ‘A’ (MULTIPLE CHOICE QUESTIONS) 1. Choose the correct answer for each from the given options: \ i) The variance of 7,7,7,7, is: * Zerov *7 #720 *75 ii) The lower limit of probability * 00 * 3 +1 * Zero iii) The data obtained from the newspape * Secondal y a * Discrete data * Primary data * Continuous da iv) Median can be located graphically by usin * Bar diagram ‘a * Histogram —* Ogive ¥PAST PAPERS XII (C) 197 4 STATISTICS v) The sum of wal “as “100 vi) The set of all possible outcomes of an experiment is called: * Sample event * Sample point * Sample space * null set vii) On tossing a die, the probability of getting 6 is: 4 “0 Ye v “i, or viii) The number of wickets taken by a bowler im 2 match is: * Inferential Variable * Discrete Variable “ * Continuous Variable * Qualitative Variable i ix)4f (x — 15) = 0 for a data then, the arithmetic mean will be: ; * 15 * zero. *1 * 150 x) P(A) + P(A’) is equal to: * Zero “A? *P(ANB) . *P(AUB) STATISTICS 2015 TIME: 1 Hours 45 Minutes (Regular & Private) (40 Marks) SECTION ‘B’ (SHORT ANSWER — QUESTION) _(25 Marks) NOTE:. Attempt any Five part questions from this Sestion. All questions carry equal marks. 2.i) Describe the sources of the collection of Primary Data. ii) The data given below shows the marks obtained by the students in Statistics: . [37 [48 [3 [79 Beale 39 [46 75_| 80 | 28 | 17 65 | 69 27_| 29 | 65 | 28 | 38 | 23 +e = 48 a7 [a [or [a [as [47 [4 oH 37 38 83 134 | 49 | 68 | 84 | 67 | 49 75 a) Construct frequency distribution taking ai interval ara TO marks. b) Find the relative frequencies. iii) For the data given below, calculate the mean of x and y where y = 2x +10. f 8 4 3 0 4 6 10 x 3 i 10 | 30 4 16 10 iy) For the following data: Year 2011 2012 2013 A 18 20 20 B 25 25 27 Cc 60 59 62PASTPAPERS XII(C)__198 Shy STATISTICS D 40 a | Compute aggregative price Index numbers using simple aggregative method taking 2011 as base year. {Ly A coin and 2 die are thrown together, “Find: a) sample spare b) the probability of getting head vi) Draw a Pie diagram for the following data on your answer script: | item Food “Clothing Rent | Medical | Mise. | Total | Expenditure , 3000 ' 1000-2000 500 700 | 7200 vii) For the data 23, 18, 28, 15, 23, 19, show that D(x — X) = 0. viii) A bag contains 6 green and 4 white balls. Three balls are drawn at random from the bag. What is the probability of getting 2 green and I white balls? OTE: Attempt any TWO questions from carry equal marks. The use of calculator is allowed. 3.a) Three coins are tossed. Prepare the sample space and find the probability of getting 2 or 3 heads. b) Two dice are rolled. Find the probability that the sum of the dots on the faces of the dice is 9. 4. Calculate the mean, the median and the mode from the following table and comment on the result. | Ci. [10-19 720-29 [30-39 [40-49 [50-59 | 60-69 [70-79 f[2if,3 {nn {2 |32 | 2s | 5. For the following data, calculate weighted Index number for the year 2011 using: i) Laspeyere's Price Index number. _ ii) Paasche's Price Index number. iii) Fisher's Price Index number. Commodities | 2010 TL 2011 | Price [Quantity | Price | Quantity Wheat | 30 5 | 45s | Sugar 120 4 | iso | 3 60 8 tT | 310 7 STATISTICS 2014 Time: 15 minutes (Regular) Max, Marks: 10 MULTIPLE CHOICE QUESTIONS 1. Choose the correct answer for each from the given options: i) The height of students of a class is: * Di e Continuous variable Wee eee PAST PAPERS XII 199 STATISTICS * Qualitative variable Fonstant ii) The data which is processed at least once is called: * Primary data * Qualitative data * Quantitative data * Secondary data “ iii) If the mean of the data with 25 observations is 40, then 5 x is: *10 * 100 * 1000 7 * none of these iv) If the mean is Sand the mode is 5 of a symmetrical frequency distribution, then the median is: 0 "sv “10 * 25 v) The sum of the deviations of observationsfrom the means is always: “Maximum — * Minimum —* Zero ¥ * Negative vi) A card is drawn at random from 52 playing cards. The probability of getting a face card is: Ns "hs 3hgv sig vii) 4 Coins are tossed together. The number of all possible outcomes is: *2 oe 4 * 8 * 16% ii) SC3 is equalto: *20* 107 * 100 “15 ix) The alphabets of the word PEN can be arranged in: #3 ways * 4 ways * Sways * 6ways¥ x) The characteristic of sample is known as: * Population * Statistic” * Parameter * variable STATISTICS 2014 TIME: | Hours 45 Minutes (Regular) (40 Marks) SECTION ‘B’ (SHORT ANSWER — QUESTION) _(25 Marks) NOTE: Attempt any Five questions from this section. All questions carry equal marks. The use of calculator is allowed 2.i) Define discrete and continuous variables. Write two examples for each. ii) The following data refers to the monthly wages (in Rs) of 25 workers. 340 [379 [331 [323 [318 [341 340 332 | 363 [311 [315 [327 [334 [340 | 358 | 340 | 338 [331 [345 | 333 [348 [329 1349 | Prepare frequency distribution by taking class intervals as 310-319, 320- 329. iii) The mean of 4 number is 5 and the mean of 3 other numbers is 12. What is the mean of these 7 numbers? iv) How many committees can be formed out of 13 women and 4 men by women and 2 men? w a Pie chart on your answer script from the following data. __ [Food [Clothing | Rent | Medical_| Other [expenditure in(Rs.) [96 132 [50723 40 350 356; PAST PAPERS XII (Cc) 200 Shen STATISTICS vi) For the data 16,12,14,18,20 show that D(x — ¥) = 0. vii) Taking 1980 as the Base year, compute price relatives of the following prices of wheat. Years 1976 | 1977 | 1978 | 1979 | 1980 | 1981 | 1982 Price Rs. | 210 | 2 23 4 25 26 27 viii) How many permutations are possible for the alphabets of the words ACCOUNTANCY" and "ECONOMICS"? ; SECTION ‘C’ (DETAILED-ANSWER QUESTIONS )(15) NOTE: Attempt any TWO questions from this section. All questions carry equal marks. The use of calculator is allowed. 3. Compute the mean, median and mode of the given frequency distribution. Weight [16-20 [21-25 | 26-30 [31-35 | 36-40 | 41-45 ‘Frequency | 4 | 6 8 14 8 6 4. Calculate: (a) Laspeyer's (b) Passche's (c) Fisher's Price Index number by taking 2011 as Base year using the following data. (Commodities | 2011 2012 | | Price | Quantity | Price | Quantity A | 6.60 240 7.10 330 B [4.15 185 4.90 210 l Cc [1.25 315 2.00 345 5. Two balanced dice are rolled together: Find the: (a) Sample space. : (b) Probability that the sum of dots on the top face of both the dices is eleven. (c) Probability of getting the same number of dots on both the dices. OR A bag.contains 4 white and 6 black balls, 3 balls are drown at random. Find the probability of getting: (a) 2 white balls and 1 black ball (b) 3 white balls (c) 3 black balls : STATISTICS 2014 Time: 15 minutes (Private) Max. Marks: 10 SECTION ‘A’ (MULTIPLE CHOICE QUESTIONS) 1. Choose the correct answer for each from the given options: i) In Paasche's Weighted price index, weight is: * Base price * Current price y * Current quantity ii) Two events which can not happen together are called: * Jcint events * Composite events * Mutually exclusive events ¥ * Conditional eventsili) A set of all possible outcomes a * Outcome * Sample space 7 * Event iv) The graph for a cumulative frequency distributi . * Histogram —* Polygon * Ogive ¥ * Line diagram ') Number of ways in which two items can be selected from four different items is: *Two * Four * Sinrv * Eight vi) The method of sample survey is used to collect: * Secondary data * Primary data ¥ * Grouped data * Quantitative data vii) When order is important, selection of different objects is called: * Tree diagram * Combination * Permutation ¥ * Multiplication Principle viii) The middle-most value of ordered observations is called: * Mean * Median ¥ * Mode * Quartile ix) The number of employees absent on a day is: * Qualitative variable * Discrete variable “ * Continuous variable * Categorical variable x) The sum of deviations of values of data from their mean is always: *Zero¥ * One * Five *Ten STATISTICS 2014 TIME: 1 Hours 45 Minutes (Private) (40 Marks) SECTION ‘B’ (SHORT ANSWER ~ QUESTION Marks) NOTE: Attempt any Five questions from this section. All questions carry equal marks. The use of calculator is allowed 2.i) The mean of 25 values is 56. If a value 82 is inchuded in the data, then find the mean of 26 values. ii) From a pack of 52 cards, a card is drawn at t random. What is the probability that the card is: (a) either a 10 ora 5? (b) either a face card or a number card? iii) Two persons claimed that their target to hit is 65 percent and 72 percent respectively. They are given a target to hit. Find the probabi the target being hit by any of them. iv) The price of a commodity for six years is given in the table. Calculate price relatives: (a) taking 2008 as base year (b) using chain base method Years 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | Price Rs. 20 21 23 28 30 L 35 vy) For the given table, construct Relative frequency and.Cumulative frequency distribution. qa Class- 101-110 | 111-120] 121-130] 131-140] 141-150 | 151-160 Interval = a ———— Sx \a————————oeeEeEeEeEeEe——( ett~—~—OSO—O PAST PAPERS XII (C. 202 shay STATISTICS _ 4 5 12 16 10 vi) Differentiate between the following: (a) Descriptive and Inferential Statistics (b) Primary and Secondary Data © vii) A coin is tossed three times. Find: (a) Sample Space (b) Probability that at least two heads will appear. viii) Two dice are rolled. Find: (a) Sample Space (b) Probability that the sum of the dots on the faces of the dia is 8. SECTION ‘C’ (DETAILED-ANSWER QUESTIONS )(15) NOTE: Attempt any TWO questions from this section. All questions carry equal marks. The use of calculator is allowed. 3. The following data represents the retail p Frequency {20 rices of 40 items in rupees: Tso [so [50 | 28 | 6s | 40 | 50 | 22 | 32 | 30 79 | 50 | 22 | 20 | 35 | 24 [25 [38 [35 | 35 “os | 20 [14 [25 [24 [48 [is | 10 [17 | 60 "2s [22 [0 | 30 [12 [30 [10 | 2 | 20 | 68 (a) Prepare a frequency distribution taking equal classes of size 14. (b) How many items have price more than Rs.51?. 4. Compute mean, median and mode for the following frequency distribution. -Class-Interval 0-4 5-9 | 10-12 | 15-19 | 20-24 | 25-29 | Frequency 12 20 | 48 10 7 3 5. Calculate Laspeyre's, Paasche's and Fisher's price index number for 2008. Commodities 2006 2008 Price Quantity Price Quantity A | 64 270 102 320 B 40 14 70 210 I c 83 | 130 95 125 OR From a bag containing 5 white and 4 black balls, 3 balls are drawn at random. Find the probability of getting: (a) 2 white balls and I black ball (b) 3 white balls (c) 3 black balls STATISTICS 2015 Time: 15 minutes (Regular) Max. Marks: 10 SECTION ‘A’ (MULTIPLE CHOICE QUESTIONS) 1. Choose the correct answer for each from the given options:BE Ee PAST PAPERS XII (C) 203 sie STATISTICS In rolling a dice, the probability of getting an odd number is: +My + Ine +d, 4 ii) The sum of deviations of observations from Arithmetic mean is always: * Maximum * Minimum *Zerov * Negative iii) The height of students of a class is: * Discrete variable * Continuous variable 7 * Qualitative variable * Constant iv) The number pf combination of 5 distinct things taken 2 at a time is: *5 *10V * 20 *30 y) The permutation of 4 distinct objects in a line is: *6 *12 14 — vi) The mode of a frequency distribution is located graphically by: * Frequency curve * Cumulative frequency curve ¥ . * Histogram * Pie diagram vii) The characteristic of population is known as: * Sample * Statis * Parameter ¥ * Variable viii) Median of 4,5,3,6,9iss~-*3. *4 9 *54 “9 ix) An index number based on more than one commodity is called: * Simple index * Composite index “ * Price relative * Link relative 2 x) A set of all possible outcomes of aa experiment is called: * Sample space ¥ * Events *Outcomes = * none of these _ STATISTICS 2013 TIME: 1 Hours 45 Minutes (Regular) (40 Marks) SECTION ‘B’ (SHORT ANSWER— QUESTION) (25 Marks) Attempt any Five questions from this section. All questions 21) “ihe number of tourists arriving in Pakistan from different counties in the year 2000 is given below. Represent this information in Multiple Bar y | USA UAE [England [Germany | Canada 1 250 100 150 150 100 | Female 175 10 30 100 75 { ii) The mean of a set of 12 numbers is 4. The mean of another set of 20 | numbers is 5. Find the combined mean of the set of 32 numbers. iii) In how many possible ways can the letters of the words 'STATISTICS' nd 'PAKISTAN' be at ged? Liv) A coin thrown together, Draw a sample space and find the tive data with examples. ). Find the A.M. iftPAST PAPERS XII (C) 204 Jenn STATISTICS (a) An observation 54 is excluded’from the data. (b) An observation 30 is included in the data. vii) Find the mean, median and mode of 2, 10,5, 11, 11, 12, 10, 11,14. and 4, viii) Construct chain base Index Number for the given data: i Year | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | | Price | 180 | 25 32 38 | 50 55 SECTI (DETAILED-ANSWER QUESTIONS )(15) i NOTE: Attempt any TWO questions from this section. All questions ~ carry equal marks. The use of calculator is allowed. \ 3. Given below are the hours that 25 men work for in a week: 36.5 | 33.0 | 298 | 384 | 244 43.2 | 315 | 363 [581 | 156 401 | 37.0 [285 | 419 [245 37.6 | 29.7 | 308 | 21.8 | 454 305 | 52.7 | 348 | 401 | 373 (i) Construct a frequency distribution, taking 8 as the size of the class interval with the first class interval as 13.0 - 20.9. (ii) Find class boundaries and class mark. y 4. Calculate the: (a) Mean (b) Median (c) Mode for the data given below: Class 50-59 | 60-69 | 70-79 | 80-89 | 90-99 | 100-109 Frequency 7 13 25 24 13. 8 5. Calculate (a) Laspeyre's (b) Pasche's (c) Fisher's Price Index Number for the given data taking 2010 as base year. [Commodities 2010 2011 | Price Quantity Price Quantity | A 10 15 12 16 | B 15 20 20 22 { Cc 25 10 30 ps STATISTICS 2013 Time: 15 minutes (Private) Max. Marks: 10 SECTION ‘A’ (MULTIPLE CHOICE QUESTIONS) | 1. Choose the correct answer for each from the given options: i) If Arithmetic mean of 5 values is 20, them sum of the values is: : *4 *10 * 80 * 100% ii) If P(A) = 0.3, then P(A’) is: * 0.6 *] *03 * O7v iii) The data which is processed at least once is called: * primary data * qualitative dataPAST PAPERS XII 205 dew STATISTICS * quantitative data * secondary data “ iv) If 4 coins are tossed together, then the number of all possible outcomes is: *2 “4 “8 “164 v) The sum of Relative frequencies is: +05 *1v “4 “100 vi) In symmetrical distribution, the mean, median and mode are always: * zero “negative —* equal ¥ * none of these vii) A set of all possible outcomes of an experiment is called: * Sample event * Sample point * Sample space ¥ : * Null set viii) A certain ordered arrangement of a group of items is called: *Factorial — * Union * Permutation * Combination ix) Three persons can be seated in a row in: * 3 ways * 1 ways * 9 ways * 6 ways ¥ Ay) The median of the data 2, -2, 3,-3, 1, -1 is: ‘ad "3 *3 *ov : STATISTICS 2013 TIME:.1 Hours 45 Minutes _ (Private) (40 Marks) SECTION ‘B’ (SHORT ANSWER - QUESTIO. fai NOTE: Attempt any Five questions from this section. All questions carry equal marks. The use of calculator is allowed 2 i) Differentiate between Primary data and Secondary data. Give at least two sources of each kind. _ ii) Differentiate between Discrete variable and Continuous variable. iii) For the data 02, 04, 06, 08, 10 verify that X(x —X) AO. iv) Construct Histogram and Frequency polygon on samt the graph paper of the following data: Class Interval 37 [812] 13-17. | 18-22 | 23.27 | Frequency 10 15 20 lomo (nas ‘alculate simple price index numbers with (a) 2001 as base year (b) ¢ prices of 200 and 2007 as base year price for the following data: Years 2001 [2002 [2003 |2004 [2005 [2006 [2007 Price (Rs) \Y 10 [15 | 20 | 25 | 30 | 35 | 40 vi) From a group of 8 boys and 4 girls, a group of 3 students is to be selected. How many combinations are possible if we select: {y (a) 2 boys and 1 girl? (b) boys only? vii) Fora certain distribution the mean‘is 40.4 and the median is 36. Find the mode using the empirical formula. viii) A fair coin is tossed 3 times. What is the probability that at least one head will appear?PAST PAPERS Xil (C) 206 shay STATISTICS SECTION ‘C’ NOTE: Attempt any Two questions from this Section. All questions carry equal marks. The use of calculator is allowed. Graph paper will be supplied on demand. 3. Complete the following table: Ca. CB. t Relative i | Frequency | i 4 aa 29 ! = 0.40 69 | 4 22 0.22 94 { 09 = z 100 4. Calculate: (i) Laspeyre's price index number (ii) Paasche's price index number (iii) Fisher's index number for the following data: (Commodities | 2003 2004 | | Price Quantity Price Quantity. | A 170 56 175, 63 | B L200 53 175 76 Cc 190 64 200 93 | D 180 13 195 27 5. From a pack of 52 well shuffled cards, a card is drawn at random. What is the probability that it is a: (i) red card? (ii) spade? (iii) queen? STATISTICS 2012 Time: 15 minutes (Regular) , SECTIO 1. Choose the correet answer for each from the given option: i) If Laspeyer's price index number is 125% and Paasehi number is also 125%, then Fisher's [deal price index nu * 130% * 100% 125% V #25 ii) The probability of drawing a diamond card randomly from a pack of 52 sist eco *Bsyv * Ys i) Two events A & B which do not occur simultancously are called: * Mutually Exclusive * Independent Events * Not Mutually Exclusiv ents * Dependent Events iv) The number of members of a family ee * Continuous variable ULTIP 's ndex ber will be:—V—OeeEeeEeEeEeEeEEeEeEeEeEeEeEeEeEeEE—E— ee PAST PAPERS XII (C) 207 ew STATISTICS * Qualitative variable + All of these v) One tossing a die, the probability of getting 6 is: *0 “1 re i, vi) When all observations of a data are negative, the mean ts: * Negative * * Positive + Negative & Positive both * none of these vii) The sum of the deviations about mean of a data is always: *Negative — * Positive * Negative & Positive both * Zero viii) The most frequent value of a data is known as: * Mean * Median * Mode ¥ * Tero ix) The probability of any event lies from: *OtolY *-Ltol * 2102 *-1t00 x) The graph of cumulative frequencies is known as: * Frequency curve * Ogive ¥ * Frequency Polygon * Histogram STATISTICS 2012 TIME: 1 Hours 45 Minutes —_ (Regular) (40 Marks) SECTION ‘B’ (SHORT ANSWER - QUESTION) _(25 Ma: NOTE: Attempt any Five questions from this section. All questions carry equal marks. The use of calculator is allowed iii) Draw a Pie-Chart for the grades obtained by the students in your answerscript. (Gradesmaar| Asti Ade ees Cre ED eT) eeieee Students [20 | 40 [| 60 | 85 [120 | 20 | 50 iv) A card is drawn at random from a pack of 52 playing cards. Find the probability of getting a red face card. v) In how many ways can we arrange the letters of the word PAKISTAN and the word ACCOUNTANCY? vi) Construct a frequency distribution taking size of class intervals as 9 and the starting point of first class interval is 126 for the given data, Also find relative frequencies and mid-values of class intervals. . 137 [152 [127 1147 [rat [1571 132_[153 146 | 142 [162 169 | 149 [135 | 166 [157 163133 [148 150 | 136 [127 162 | 152 145 | 154 | 44 126 | 139 | 126 | 158 | 147 134 [148 [153 | 161 ]136 [147 | 142 | 159 146 [138 [144 [166 [141 [143 [136 [147 ii) The given table shows the prices of a commodity for 6 years. Construct the Link Relatives._ PAST PAPERS XII (C 208 jugs STATISTICS Years 2000 | 2001 | 2002 | 2003 [2004 [2005 | 2006 Price (Rs) | 45 | 52 | 58 | 64 | 72 | 80 | 38 | viii) Differentiate between Population and Sample. SECTION ‘C’ (DETAILED-ANSWER QUESTIONS )(15 NOTE: Attempt any TWO questions n this section. All questions carry equal marks. The use of calculator is allowed. 3. Three coins are tossed simultaneously. (a) Construct sample space using Tree Diagram. | (b) (i) Find the probability of getting No Head. | (ii) Find the probability of getting at least One Head. 4. For the given data: Calculate the following weighted index numbers for the year 2009. (i) Laspeyre's price index number (ii) Paasche's price index number (iii) Fisher's Ideal price index number [Commodities 2010 2011 | Price [Quantity | Price [Quantity Sugar | 32 5 45 4 Oil [_120 4 150 3 Milk | 42 10 48 8 [Mutton | 220 12 350 7: 5, For the given frequency distribution: (a) Calculate the: (i) Mean (ii) Median (iii) Mode (b) Show mode with the help of graph. [ Age 5-14 | 15-24 [25-34 [35-44 | 45-54 ? [Frequency | 5 1 | 20 | 18 6 STATISTICS 2012 Time: 15 minutes (Private) Max. Marks: 10 SECTION ‘A’ (MULTIPLE CHOICE QUESTIONS) 1. Choose the correct answer for each from the given options: i) The letters of the word CAT can be ar ranged in: * 3 ways * 4 ways 5 ways * 6 ways ¥ ii) Me an be located graphically by using: * Bar diagram “OgiveY —* Histogram — * Pie diagram iii) The base year index is always: * 98% * 99% * 100% ¥ * 101% iv) The word Statisties is nowadays used in: * two senses ¥ * three senses * four senses * five sens; y) The mean of 4, 4.4.4, 4 *O #3 RA *5 vi) The number of students in a class is: * Continuous variable & Discrete variable ¥ —* Qualitative variable * none of thesex vii) If the range of a data is 10 and the maximum value is $0, then the PAST PAPERS XII(C) 209 jew STATISTICS minimum value “48 20 “3ov 50 viii) A card is drawn at random from 52 cards. The probability of getting an Ace is: *Ih3P "Th "I "4h ix) For a pie diagram, the sum of all sector angles is: * [80° * 200 * 270° * sor x) A data which is collected for the first time is called: * Primary data “ # Secondary data * Continuous data * none of these . STATISTICS 2012 TIME: 1 Hours 45 Minutes (Private) (40 Marks) SECTION ‘B’ (SHORT ANSWER - QUESTION) (25 Marks) NOTE: _ Attempt any Five questions from this section. All questions carry equal marks. The use of calculator is allowed 2 i) Differentiate between Primary data and Secondary data. ii) Mean of the data of 25 values is 45.6. Find: (a) the mean, if a value 30 is included in the data. (b) the mean, if a value 12 is excluded from the data. _ ii ind the number of permutations of the letters of the word 'STATISTICS'. iv) Find the Mean, Median and Mode of 1, 3, 4, 7, 9, 10, 11, 11, Ba 14,10 and 2. v) Draw a pie diagram for the following data: Item A B Cc D | E Frequency 16 20 12 24 | ~<18 vi) A card is drawn randomly from a pack of 52 cards. What is the probability that the card is (a) Black? (b) King? ree balanced coins are tossed together, find (a) the Sample Space ) probability that there is no tail. —~ i) Construct simple price index numbers for the following data by ching 2007 as base year: [Year 2007 | 2008 | 2009 | 2010 | 201% MK [Price (Rs) 216 [249 | 264 | 2761288 Attempt any T equal marks. The use of calculator is allowed. (i) Mean (ii) Median (iii) Mode for the following data and also comment about the distribution. cond 40-49 | 50-59 | 60-69 _|.70-79 [80-89 [90-99 f 8 13 24 24 | 13 8 4. Calculate:PAST PAPERS XIl (C) 210 diay STATISTICS Laspeyre's index number (ii) Paasche (iii) Fisher's Index number for the following data: Commodities 2009 2010 | Price [Quantity | Price | Quantity | A is 50 20 40 | B 1B 40 29 35 | Cc 2 45 aw | 25 5. Two balanced dice are rolled together. Find: (i) The Sample Space i) The Probability that sum of dots is an even number. ility that sum of dots is at least 9 (iv) The Probability that sum of dots is at most 4. STATISTICS 2011 Time: 15 minutes (Regular) Max. Marks: 10 SECTION ‘A’ (MULTIPLE CHOICE QUESTIONS 1. Choose the correct answer for each from the given optioi i) If the mean of a data with 25 observations is 40, then the Sx is equal to: *50 * 100 * 1000 * none of these ii) If Laspeyre's Index number 92.16% and Paache's Index Number is 81.4% then Fisher's Index Number will be: * 86.1% * 85.44% * 8.77% * none of these iii) 5 students can be seated in a row in: * 4 different ways * 5 different ways * 24 different ways — * 120 different ways.” iv) P (A) + P(A’) is equal to: viv *0 * 05 * none of these vy) [f A and B are two independent events and P (A) = 0.6 and P(B) = 0.25, then P (ANB) is: * 0.85 * O15 ¥ * 0.86 * none of these vi) A set of all possible outcomes of an experiment is called: * Sample space ¥ * Subset * Empty set * none of these vii) A data may have more than one: * Median * Mean * ModeY —* none of these viii) The wages of workers in a factory represent: * Quantitative data ¥ * Qualitative * Discrete data * Continuous data ix) A frequency polygon may be drawn on: * Histogram ¥ * Bar diagram J x) The sum of the deviations from mean of the data is always: *Ov ae a5 +7