Chapter 14

Statistics

1. The marks obtained by 25 students in an examination are given below:

370, 290, 318, 410, 378, 480, 375, 315, 225, 288, 325, 355, 402, 382, 178, 253, 154, 306,
360, 328, 440, 425, 380. 198, 230.
Form a continuous frequency table with one class interval as 200 – 250.
2. The class marks of a distribution are 37, 42, 47, 52. Determine the class size and class limits
of the last class marks.
3. The blood groups of 30 students of class IX are recorded as follows:
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
Represent this data in the form of a frequency distribution table. Which is the most
common and which is the rarest blood group among these students?
4. The following are the runs made by 18 players in one day cricket match:
79, 28, 45, 99, 3, 46, 8, 0, 3, 7, 24, 73, 122, 46, 27, 16, 7, 3.
Form a frequency table for above data with equal class intervals one of these being 0 – 25
(excluding 25)
5. Two coins were tossed 20 times simultaneously. Each time, the number of ‘Heads’ occurring
was noted down as follows:
0, 1, 1, 2, 0, 1, 2, 0, 0, 1, 2, 2, 0, 2, 1, 0, 1, 1, 0, 2
Prepare a frequency distribution table for the data.
6. Convert the following frequency distribution into a continuous grouped frequency table:
Class interval Frequency
150 – 153 7
154 – 157 7
158 – 161 15
162 – 165 10
166 – 169 5
170 – 173 6
In which intervals would 153.5 and 167.5 be included?
7. A company manufactures car types of a particular type. The lives (in years) of 40 such tyres
are as follows:
2.6, 3.0, 3.7, 3.2, 2.2, 4.1, 3.5, 4.5, 3.5, 2.3, 3.2, 3.4, 3.8, 3.2, 4.6, 3.7, 2.5, 4.4, 3.4, 3.3, 2.9,
3.0, 4.3, 2.8, 3.5, 3.2, 3.2, 3.9, 3.2, 3.2, 3.1, 3.7, 3.4, 4.6, 3.8, 3.2, 2.6, 3.5, 4.2, 2.9, 3.6.
Construct a continuous grouped frequency distribution for the above data of equal class size
and with first class interval as 2 – 2.5 (2.5 is not included)
8. Convert the following discontinuous class intervals into continuous class intervals:
Class interval 1 – 6 7 – 12 13 – 18 19 – 24
9. The following data gives the weights 9in grams) of 30 oranges picked from a basket:
106 107 76 109 187 95 125
92 70 139 128 100 88 84
99 113 204 141 136 123 90
115 110 97 90 107 75 80
118 82
Construct a grouped frequency distribution table taking class size equal to 20 in such a way
that the mid-value of the first class is 70.
From the frequency table, find the number of oranges:
(a) Weighing more than or equal to 180 grams (b) less than 100 gram
10. To solve a problem, the time taken (in seconds) by the students are as follows:
37, 31, 27, 18, 59, 45, 54, 40, 32, 43, 39, 49, 45, 40, 59, 53, 52, 50, 40, 59, 60, 23, 21, 20, 22.
Construct a frequency table with equal class width and one of the class intervals as 25 – 32,
(not include 32) for the above.
11. Draw a bar graph for the given expenditure of a family on different heads in a month:
Head Expenditure (in Rs.)
Food 4000
Education 2500
Clothing 1000
House rent 3500
Others 2500
Savings 1500
12. Construct a frequency polygon for the following data:
Age Number of persons
0–4 3
4–8 6
8 – 12 8
12 – 16 10
16 – 20 8
20 – 24 5
24 – 28 3
13. Thirty children were asked about the number of hours they watched TV programs in the
previous week. The result were found as follows:
1, 6, 2, 3, 5, 12, 5, 8, 4, 8, 10, 3, 4, 12, 2, 8, 15, 1, 17, 6, 3, 2, 8, 5, 9, 6, 8, 7, 14, 12
Make a grouped frequency distribution table for this data, taking class width 5 and one of
the class intervals as 5 – 10. Also, draw a histogram for it.
How many children watched television for 15 or more hours a week?
14. If mean of 5, 9, A, 17, and 21 is 13. The find the value of A. [13]
15. Draw a histogram for the given data:
Class interval Frequency
20 – 25 21
25 – 30 22
30 – 35 50
35 – 40 75
40 – 45 67
45 – 50 51
50 – 55 18
16. Study the following bar graph and answer the given questions:

(a) In which year, was the production of wheat maximum and how much?
(b) What is the ration of the maximum production to that of the minimum production?
17. The histogram given below shows the marks obtained by students in a test conducted
during the remedial classes in the school:
 Using above histogram, make a frequency table. Also, answer the following questions
(a) How many students obtained marks less than 40?
(b) How many students obtained marks 50 and more?
18. Using the following histogram, prepare a grouped frequency distribution table:

19. The heights of employees in an office are as follows:

Height (in cm) No. of employees
130 – 140 8
140 – 150 18
150 – 160 20
160 – 170 5
170 – 180 4
180 – 190 3
Draw a histogram and frequency polygon for the above table
20. The runs scored by two teams A and B on the first 60 balls in a cricket match are given in the
table
Represent the data of both the teams on the same graph by frequency polygons.
No. of balls Team A Team B
1–6 3 6
7 – 12 2 7
13 – 18 9 3
19 – 24 5 11
25 - 30 6 6
31 – 36 10 7
37 – 42 6 4
43 – 48 12 5
49 – 54 3 9
55 – 60 1 11
21. The median of the following observations arranged in ascending order 14, 18, x + 2, x + 4,
30, 34 is 24. Find the value of x. [21]
22. The weight (in kg) of 15 students are 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42 and
30. Find the median of the data. If the weight 44 kg is replaced by 46 kg and 35 kg is
replaced by 37 kg, find the new median.
23. The following table shows the life of 400 neon lamps:
Life time (in hours) No. lamps
300 – 400 14
400 – 500 56
500 – 600 60
600 – 700 86
700 – 800 74
800 – 900 62
900 – 1000 48
(a) Represent the above information with the help of a histogram and a frequency polygon.
(b) How many lamps have life time of 700 hours and more?
24. Draw a frequency polygon to represent the given data:
Life time (in hours) No. lamps
10 – 15 450
15 – 20 400
20 – 25 850
25 – 30 900
30 – 35 600
35 – 40 455
40 – 45 220
25. Draw a frequency polygon and a histogram for the following table:
Class interval Frequency
50 – 55 12
55 – 60 8
60 – 65 14
65 – 70 10
70 – 75 6
26. Draw a frequency polygon for the following data:
Class 0–5 5 – 10 10 – 15 15 – 20 20 - 25
Frequency 16 40 32 24 8

Prepare a table to show the actual expenses in each head and hence draw a bar graph.
27. For the following data, construct a histogram and frequency polygon:
Class interval Frequency
10 – 14 300
15 – 19 980
20 – 24 800
25 – 29 580
30 – 34 290
28. The mean of 15 numbers is 18. If one number is included, their mean is 19. Find the
included number. [34]
29. Draw a histogram and frequency polygon for the following distribution:
Marks obtained No. of students
0 – 10 7
10 – 20 10
20 – 30 6
30 – 40 8
40 – 50 12
50 – 60 3
60 – 70 2
70 – 80 2

30. The length of 70 leaves of a plant are measured in millimeters and the data is represented
in the following table:
Length (in mm) No. of leaves
118 – 126 9
127 – 135 12
136 – 144 15
145 – 153 18
154 – 162 7
163 – 171 5
172 – 180 4
Draw a histogram to represent the given data. Is it correct to conclude that maximum number
of leaves is 153 mm long? Why?

31. Given below are the seats won by different political parties in the polling outcomes of a
state assembly election:
Political party A B C D E F
Seat won 75 55 17 29 10 37
(a) Draw a bar graph to represent the polling results.
(b) What is the difference between maximum and minimum of seats won by two parties?
32. The mean of 10 numbers is 55. If one more number is included, their mean becomes 60.
Find the included number. [110]
̅
33. The mean of n – observations is 𝑋. If constant “a” is subtracted from each observation, then
show that the new mean “𝑋̅ – a”.
34. In a mathematics test given to 19 students, the following marks (out of 100) are recorded :
75, 62, 88, 55, 90, 95, 85, 69, 78, 90, 95, 90, 95, 80, 71, 44, 57, 68, 90.
𝟏𝟒
Find the mean, median and mode of this data. [mean = 77𝟏𝟗 ; median = 80 ; mode = 90]
35. The scores of an English test (out of 100) of 20 students are given below:
75, 69, 88, 55, 95, 88, 73, 64, 75, 98, 88, 95, 90, 95, 88, 44, 59, 67, 88, 99.
Find the median and mode of this data. [median = 88, mode = 88]
36. The mean of 100 observations is 24. If 6 is added to each of the observations and then each
of them is multiplied by 2.5, find the new mean. [75]
37. Find the value of p, if the mean of the following data is 40.4: [p = 10]
Variable (x) 10 20 30 40 50 60 70
Frequency 3 8 12 5 p 7 5
38. There are 20 students in a drama class. The mean age of 12 students is 18 years and the
mean age of remaining 8 students is 23 years. Find the mean age of all students in the
drama class. [20 years]
39. The mean monthly salary of 10 member of a group is Rs. 1445. One more member whose
monthly salary is Rs. 1500 has joined the group. Find the mean monthly salary of the 11
members. [Rs. 1450]
40. The median of the following observations, arranged in ascending order, is 25. Find x.
11, 13, 15, 19, x + 2, x + 4, 30, 35, 39, 46. Also, find mean. [ x = 22 ; mean = 25.8]
41. It is given that the mean of five numbers is 27. If one of the numbers is excluded, the mean
gets reduced by 2, find the excluded number. [35]
42. The marks scored in a competitive examination (out of 200) are given as below:
110, 115, 95, 110, 145, 150, 175, 185, 175, 110, 115, 179, 185, 175, 110, 150, 195, 190, 110,
175, 190.
Prepare a frequency distribution table and hence find the mode of the data. [110]
43. If the mean of the following data is 20.2, find the value of p. [p = 20]
x 10 15 20 25 30
f 6 8 p 10 6
44. The average weight of A, B and C is 45 kg. If the average weight of A and B is 40 kg and that
of B and C is 43 kg, find the weight of B. [31 kg]
45. The mean of 21 numbers is 15. If each number is multiplied by 2, what will be the new
mean hence state the relation between the new mean and the old mean? [30, 15]
46. If the mean of the observations x + 1, 2x + 3, 2x + 7, 2x + 11is 30, find the mean of the last
two observations and median of all the observations. [37, 33]
47. A man spends Rs. 18000 monthly on an average for the first four months and Rs. 20,000
monthly for the next eight months and saves Rs. 56,000 in a year. Find his average monthly
salary. [Rs.24000]
48. The median of the following observations arranged in ascending order is 24. Find x.
14, 18, x + 2, x + 4, 30, 34
Using the value of x, find the mean of the above data. [x = 21 ; mean = 24]
49. Find the mean of all prime numbers lying between 20 and 30. [26]
50. The point scored by a basketball team in a series of matches are as follows: [14]
17, 2, 27, 25, 5, 14, 18, 10 Find the median.
51. The mean of 25 observations is 36. Out of these observations, the mean of first 13
observations is 32 and that of the last 13 observations is 40. Find the 13th observation. [36]
52. Find the median of the following data; [32, 35]
19, 25, 59, 48, 35, 31, 30, 32, 51
If 25 is replaced by 52, what will be the new median?
𝟓
53. The following observations have been arranged in ascending order: [x = 53 ; mean = 51 𝟔]
14, 19, 23, 38, 40, x – 2, x + 2, 62, 68, 74, 85, 93.
If the median of this data is 53, find value of x and also find their mean.
54. The following runs were scored by all the 11 players of a cricket team during a match:
36, 55, 12, 110, 14, 72, 69, 20, 18, 25, 0
Find the mean median and mode of the data. [mean = 39.1, median = 25, No mode]
55. In a Mathematics test given to 15 students, the following marks (out of 90) are recorded:
41, 39, 48, 52, 46, 62, 54, 40, 88, 52, 86, 40, 42, 52, 60.
Find the mean median and mode of this data. [mean = 802/15, median = 52, mode = 52]
56. Find the missing frequencies p and q in the following frequency distribution, if it is known
that the mean of the distribution is 1.46: [p = 76, q = 38]
x 0 1 2 3 4 5 Total
f 46 p q 25 10 5 200
57. Find the mean of all factors of 30. [9]
58. The mean age of 3 students is 21 years. If the ratio of their ages is 2: 3: 4. Then find the ages
of the students. [14 years, 21 years, 28 yeas]
59. If the mean of the following distribution is 6, find the value of p. [p = 7]
x 2 4 6 10 P + 5
f 3 2 3 1 2