La ‘ENTRAL TENDENCY 235 ir almost absurd or ficticio ,e 1 ‘us, For family and two persons in other family: "e's there are seven f e there persons in one i urd because persone thinet be arithmetic mean will be 4.5, which in fractions. "F ttis generally believed that th = 6 arithmetic ii forall general purpose, angtettdalways bo used unless there isa aes mmended inthe following situations rest However, arithmetic mean is 1. When the frequency distribution is symmetrical. 2, When we need a stable ave, da rage. 3. When other measures such . tion are to be computed later. a8 standard deviation coefficient of correla- EXERCISE Mean |. Calculate arithmeti i i Le alculate arithmetic nossa tom the following marks obtained by 10 students in Roll No. eae a ee 5 6 7 8 9 1 Marks obtained 80 28 82 1 18 2 25 1b 26 Ie [Ans, X = 22 marks) 2 Calculate the arithmetic mean from the following frequency table - Size 1 2 oan ae pte g earn eta entg Frequency () 2 60 101 162 205 15 79 40 1 (Ans. X=4.81) 3. 100 studenta gave donations as follows in a function of a school. Find average per student : 10 students donate % 5 each 15 students donate % 4 each 24 students donate % 3 each 30 students donate % 2 each 21 students donate % 1 each [Ans. 63) 4. The cost of production of sugar-cane in various holdings is given in the following frequency distribution. Calculate arithmetic mean : Cost : 2-6 610 10—14 1418 18-22 2226 26—30 30-34 Freq : $10.47 (S286 V5 18) 88 Pore i (Ans. X= 19.21) 5. Determine arithmetic average in the following distribution showing income in thousand rupees per month of 34 persons : Income (in thousand]: 0-2 24 46 6-8 8-10 10/1212 14 3 7 Bs outlets cen 208d No. of Persons lAns, X= 6 thousand) 8. Calculate mean from the following data : Marks : 1-10 rtd ay eo 3140 41-50 5160 3 No. of Students : 2 [Ans. X=29.0 marks} 7, Calculate arithmetic mean from the following data : : - = 0—20 20—30 Tempera. _ 30) —30-{-20) -20-(-10) -10-0 0-10 10-00 20, ture (CO) 40-(— 30) 42 65 a 10 2B (Ans, X=4.29°C] No. of Days__BUSINESS STATISTICS 8. Calculate arithmetic mean from the following data : More than : 85 70 55 40 No. ofPersons =: 1 4 30 74 9. Calculate arithmetic mean from the following data : Wages lin #(Less than) : 50 70 90 110 No. of Workers : 80 46 65 85 10. Calculate arithmetic mean from the following data : Lessthan: 10 20 30 40 50 60 9 p Freq. : 15 = 300 53751000 : ; Uns. 255 11. Calculate arithmetic mean from the following data (age in years) More than eo 10 15 20 25 No. of Persons 7100 9 8 71 «51g tans. X= 18.45 ean) 12. Calculate arithmetic mean from the following data : Wages (in No. of Workers Less than 48 5 Less than 56 12 48—64 29 64 and above 31 72—80 8 80 and above 19 88 and above [Ans X=63 13, The following table given the made population of Varanasi and Agra in 21 Caleulate the average age of males in Varanasi and Agra separately : Age group : 0—5 5-10 10—1515—2020—3030—4040—50 50-60 60-80 (ear) Population : of Males in thousands Varanasi 4 18 18 #18 33) «29 «647 1 4 Agra : 9 8 8 7 1B 12 9 6 4 {Ans. Varanasi 26,52 year; Agra 27.12yee) 14, Celeulate mean (by short-cut method) expenditure from the following data: eg Expenditure below rupees: 10 15 20 ie No. of Students P86 16 28 38 Tans. X= 1298 15. Caleulate mean for the following frequency distribution : » Marks less than =: 10 20 30 40 50 60 70 8 No ofStudents : 5 14 27 §2 68 70 _13 re) [Ans, X= 9447 16. Calculate mean from the following distribution : Marks less than; 20 30 40 50 60 70 No.of Students: 8 20 35 85 69 80 inst (Ame Taking lower mit as 10, however, ong ti 17. Calculate mean of the following data : 150 Salary (less than®) : 50 10 90 110 130400 No. of Workers : 30 46 65 85. 95 oz xe" 18. Compute arithmetic mean from the following data : Value : 0-10 0-20 "0830 0-40 0-50 e Frequency : 8B 18 25 37 42 qe [Ans-.__ STATISTICAL AVERAGES : MEASUR STATISTICAL AVERAGES MEASURES OF Gri TENDENCY 237 Find mean fr the filling cumulative tequeney diastase 19 Markslessthan =: 10 20 39 memes | 3 8 oR eRe Be Calculate arithmetic mean from : Ans, X=51.75 Marks} cae an from the following table - & 15 Frequency : 15 2 |B = % 7 gi, Calculate mean for the following frequency distribution : ner Oe ; ate 16—17 18-20 2124 25-29 30-34 35-39 sa Mo 165000. 90 32, Calculate mean from the following data : ae eel coe 10720 10-80 10-40 10-50 1960 10—70 10-80 1090 ‘ 560 87) 124187146 «150 4s, Calculate mean from the following frequency distribution; “™" *" “9% eee wt ake S76 68 sn N25 15-18 a 3 Class 1820 20-22 22-94 24-29 29°90 90°04 o436 Fequeny =: 12 10 8 9 6 3 (Ans. Make equal class-intervals, X= 34, Calculate mean from the following table : sonal serene A Class : 1-5 6-10 1115 16—20 2125 26—30 3135 36—40 4145 Frequency =: , 10 16 32 24 18 10 5 1 (Ans. X= 20.36] 25, Find mean from the following data : Sales more than(in®?) : 15 20 25 30 35 40 45 No, of Salesmen : 40 37 31 28 13° 6 0 (Ans, X =% 31.25] 26, Find mean from the following data : Marks less than : 10 20 30 40 50 60 60 andover No. of Students 8 22 44 68 84 96 4 = (Ans. X=32.8] 27. Caleulate mean from the following data : (i) without making equal class- intervals and (ii) making equal class-intervals : Class 12 8 4 5ST 710 10-15 15-20 20-25 Frequency arse git tenga 5 10) By aed [Ans, (i) X = 12.38, (ii) X= 12.21,] 28. The mean of the following series is 46.06. Find out the unknown weight : Weight 20 30 2 50 60 70 0 9 5 3 Frequeney 2 4 1 40) 29. If the mean, X= 68.25 for this series, then find out the value of the blank place : Wages(inrupees): 50 58 60 65 i 7 ie 1 : 35 No. of Workers : 2 20 5 [Ans. 75] 30. If the mean of the following distribution is 47.95, find the unknown frequency : 40-55 5570-70-85 85—100 Class : 10-25 25-40 3 ; 2 44 a Frequency : 6 20 [Ans. 26]* 238 BUSINESS STATISTICS ihc 31. Mean of the distribution is 25. Find out the missing frequency See Class Interval Frequeney 0—10 3 10—20 7 | 20-30 20 30—40 6 | 40—50 2 50—60 1 82, The arithmetic mean of the following distribution is 67.45 inche. Find ¢, 4™% | Height (inch) Frequency 60—62 15 63—65 54 66—68 f 69-71 61 214 24 (Ans. 1267 e1y Combined Mean 88. The average salary of all workers of a company was % 3,000. The average of men was 3,200 and that of women was & 2,200. Find the percentage of meq and women in the company. (Ans. Men 80%; Woman 205 | The mean of 15 numbers is 15. If the two numbers 18 and 12 are excluded, thea what will be the mean of the remaining numbers? (Ans. 15 }. A tennis club wants to compare the average performance of its 3 competition teams with that of another club. In the past year, its A grade team played 45 games and wm, 73.3% of them, the B grade team played 40 games and won 75% and C grade team played 35 games and won 94.3% of them. What is the group average? (Ans, 80%) 36. Average daily production of cycle tyres in a factory for the first 20 days of a month was 390 and for the remaining 10 days of the month the average daily producti was 400 tyres. Calculate the average daily production for the month as a whele. [Ans, 393.33 tyres) 37. The average monthly sales for the first eleven months of the year in respect of certain salesman was t 12,000 but due to his illness during the last month, the average monthly sales for the whole year came down to ¢ 11,375. What was the value of his sales during the last month? (Ans, & 4,500] 88. A batsman has a certain average of runs for 15 innings. In the 17th inning, makes a score of 85 runs, thereby increasing his average by 3. What is the averaét after the 17th inning? {Ans.37 no) 39. Aman has 7 children. When their average age was 12 years, the child who was years of age died. What was the average of the surviving children 5 years tr the death of the above child? Ans. 18 ye4 40. An investor buys Z 1,200 worth of shares in a company each month. During first five months he bought the shares at a price of 2 10, 2 12, % 15%, 20 ant per share. After 5 months what is the average price paid for the shares LA ad (ans. 4 41, The mean wage of 100 labourers working in a factory, running in two siete and 40 labourers respectively % 38. The mean wage of 60 labourers Wort g, first shift is € 40, Final the mean wage of 40 labourers working in the seeds 6,0,40088 & & 42. Goals scored by a football team in successive matches are 5, 2, 4, 3: tbat What is the number of goals the team must score in the next match in order) the average comes to 4 goals per match. tans. 6 48. The mean weight of 80 students in a class is 56.25 kg. The mean weight of DO in the class is 60 kg. and that of the girls is 50 kg. Find out the numbe © and the girls in the class. [Ans. Boys 60, adLL STATISTICAL AVERAGES : MEASURES OF CHNTRAL TENDENCY 239 a erag mack in Stentice of 10 atadant of a class was 68, A now student took admis 8 two oxisting studonts loft c th Pe ueicistuslonta ware 40 sal 30 sesce eee neal, tho collogo. If the manning talents, and 39 respectively, find the nar ns, Calculation of General and Standardised Raton 4s, compare health, conditions ete cae P and Q from the following informations bwn P 7 Age-srouP | Population Toon 2 Ave td Deaths Population Deaths os heme 100 10,000 160 5 5 $5,000 175 26,000 100 25-5! , 225 30,000 250 _5 & above _|_— __20,000. 150 15,000 200 ‘Total 1,00,000 650 80,000 | 700 : Tan DR: Town P = 6.50, Town Q= 8.76, SDI of Town Q = 9 248) 4g, Determine that which town’s population shows better employment conditions from the following informations : 0 i Town A Town B Asesroup | population | No. ofemploy- | poputation | No. of employ- . _ment | Topulation ment_ 0-10 5,000 250 200 10-30 15,000 300 360 30-50 25,000 400 250 50—60 10,000__|___200 200 Total 55,000 1,150 1,000 of town (4.77) TAns. : GER: Town A = 20.91, Town 47, State which college result is better from the following information . College M College NT Examination |“Appeared Passed. ‘Appeared | Passed B.Se. 250 200 300 280 BEd. 300 280 150 140 B.Te. 150 130 250 240 B.A 200 190 200 160 College N = 91.11%, ‘SPP of College N = 90.81%) TAns. : GPP = College ‘M = 88.89%, 48. From the following data calculate Standard ‘Death Rate of Town ‘A’ and Town ‘BY and also state which town is more healthier ? ‘Standard Bee Deatl ite. Agegroup Population Town A ‘Town B 0-15 2,500 25 30 15—30 4,000 16 20 30—40 5,000 10 15 4 3,000 60. | 10 “SDR Town A= 24.31, Town B= 90.34) (Ans 48. General Death Rate of town Aand town B are 10.50 and 162 respectively. You are required to calculate : (@ Missing death rate of town A. (ii) Missing population of town B. (ai) Standard Death Rate of town B. ‘A (Standard) ~ ‘Town B (Local) _Ascerou | -ppulation ad ate | Population | Death Rate — 10—20 20 60,000 5 20—40 10 20,000 40-50 10 ? 5055 2 1,00,000 S575 4051. BUSINESS STATISTICS Weighted Mean ; Cann an ein, ema ish 60, Business Studies 75, 80, Beono et ee eosin emnarks ifweights of these subjects are 2, 2, Land 1 oe cy } IAna Compute the weighted arithmetic mean of the index number from the data a a below : Group tudes No. Weight — 4 Food 260 Clothing 280 : Fuel and light 340 § House rent 360 6 Miscellaneous | ns ey Calculate simple and weighted arithmetic averages of prices from the foloygg data and comment on. them + Quantiiy on rie Article sumed (ke) | (per kg Flour en 4 Ghee 40 Sugar ang 10 Potato 2 Oil 50 20 TAns. €15.2;297y, . Calculate weighted mean from the following data : Salay (9 Weight Below 50 30 Below 70 46 Below 100 65 Below 110 85 Below 120 95 Above 120, 5 or . A candidate obtained the following percentages of marks in differents subjects ia the Half yearly examination : . English 46%, Statistics 67%, Cost Accountancy 72%, Economics 58%, Income-t* 53%. Itis agreed to give double weights to marks in English and Statistics as compare! to other subjects. Calculate simple and weighted arithmetic mean. oA (Ans. Simple Mean = 59.2, Weighted Mean = Mathematics 80, Economics 60, Hindi 55, Social Science 60. Find the wel Mean of candidate's percentages if weights of 5, 4, 3, 2, 1, respectively are all to these subjects. Find his unweighted mean as well. [Ane, Xy = 68% 658) ‘The following table gives the distribution of 100 accidents during seven 4%. the week of @ given month. During the particular month there were five Mondat® ‘Tuesdays and Wednesdays and only four each of other days, Calculate the of accidents per day : . A student obtains the following percentage in an examination : English " jotted D No. of Acci- No, of aes sch! dents Days dents Sunday 26 Th 8 Monday 16 ease 10 Tuesday 12 18 Wate a _ ‘SaturdaySTATISTIC oy ICAL AVERAGES. : MEASURES OF — F CENTRAL TENDENCY 241 qe examination ie aoa to decide the award of a scholar: hip, ight of various subj ere different. The marks obtained by 3 andi a en pelow =. candidates are give O subiet Marks (A) “|” Marka (B) | Marke (©) Statistics 4 63 liebe eit ene te (eG Mathematics 65 64 10 Economics 58 56 63 Hindi 70 80 52 (Ans. A—63, 3; B—62.4; C648, So O will get scholarship} 58. From the results of two colleges ‘A’ and ‘B’ given below state which of them is er: Class College ‘A’ College ‘B’ Appeared Passed Appeared Passed Mom. 200 180 480 400 MSe. 120 90 400 320 BCom. 240 150 320 200 BSc. 300 400 400 280 (Ans. College ‘A’ = 75%; College ‘B’ 72.15%. Therefore, college ‘A’ is better.]