## Chapter 7 Statistics R.D. Sharma Solutions for Class 10th Math Exercise 7.5

1. Find the mode of the following data:
(i) 3,5,7,4,5,3,5,6,8,9,5,3,5,3,6,9,7,4
(ii) 3, 3, 7, 4, 5, 3, 5, 6, 8, 9, 5, 3, 5, 3, 6, 9, 7,4
(iii) 15, 8, 26, 25, 24, 15, 18, 20, 24, 15, 19, 15

Solution

(i)

(ii)

(iii)

2. The shirt sizes worn by a group of 200 persons, who bought the shirt from a store, are as follows:
Shirt size: 37  38  39  40  41  42  43  44
Number of persons: 15  25  39  41  36  17  15  12
Find the model shirt size worn by the group.

Solution

3. Find the mode of the following distribution.
(i) Class-interval: 0-10  10-20  20-30  30-40  40-50  50-60  60-70  70-80
Frequency: 5   8  7  12  28  20  10  10
(ii) Class-interval: 10-15  15-20  20-25  25-30  30-35  35-40
Frequency: 30  45  75  35  25  15
(iii) Class-interval: 25-30  30-35  35-40  40-45  45-50  50-60
Frequency: 25  34  50  42  38  14

Solution

(i)

(ii)

(iii)

4. Compare the modal ages of two groups of students appearing for an entrance test:
Age (in years): 16-18  18-20  20-22  22-24  24-26
Group A: 50  78  46  28  23
Group B: 54  89  40  25  17

Solution

5. The marks in science of 80 students of class X are given below: Find the mode of the
marks obtained by the students in science.
Marks: 0-10  10-20  20-30  30-40  40-50  50-60  60-70  70-80  80-90  90-100
Frequency: 3  5  16  12  13  20  5  4  1  1

Solution

6. The following is the distribution of height of students of a certain class in a certain city:
Height (in cm): 160-162  163-165  166-168  169-171  172-174
No. of students: 15  118  142  127  18
Find the average height of maximum number of students.

Solution

7. The following table shows the ages of the patients admitted in a hospital during a year:
Age (in years): 5-15  15-25  25-35  35-45  45-55  55-65
No. of students: 6  11  21  23  14  5
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Solution

8. The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:
Lifetimes (in hours): 0-20  20-40  40-60  60-80  80-100  100-120
No. of components: 10  35  52  61  38  29
Determine the modal lifetimes of the components.

Solution

9. The following table gives the daily income of 50 workers of a factory:
Daily income (in Rs) : 100-120  120-140  140-160  160-180  180–200
Number of workers:  12   14   8   6  10
Find the mean, mode and median of the above data

Solution

10. The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret, the two measures:

Solution

11. Find the mean, median and mode of the following data:
Classes: 0-50  50-100  100-150  150-200  200-250  250-300  300-350
Frequency:  2   3   5   6  5   3  1

Solution

12.  A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised in the table given below. Find the mode of the data :
Number of cars : 0-10  10-20  20-30  30-40  40-50  50-60  60-70  70-80
Frequency : 7  14  13  12   20   11   15   8

Solution

13. The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.
Monthly consumption : 65-85  85-105  105-125  125-145  145-165  165-185  185-205
(in units)
No. of consumers:  4  5  13  20  14  8  4

Solution

14. 100 surnames were randomly picked up from a local telephone directly and the frequency
distribution of the number of letters in the English alphabets in the surnames was obtained
as follows:
Number of letters: l-4  4-7  7-10  10-13  13-16  16-19
Number surnames: 6  30  40  16  4  4
Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.

Solution

15. Find the mean, median and mode of the following data:
Classes:  0-20  20-40  40-60  60-80  80-100  100-120  120-140
Frequency: 6  8  10  12   6   5   3

Solution

16. The following data gives the distribution of total monthly houshold expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:

Solution

17. The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Solution

18. The frequency distribution table of agriculture holdings in a village is given below :
Area of land (in hectares) : 1-3  3-5 5-7 7-9 9-11 11-13
Number of families : 20  45  80  55  40  12
Find the modal agriculture holdings of the village .

Solution

The maximum class frequency is 80. The class corresponding to this frequency is 5-7.
So, the modal class is 5-7.
l(the lower limit of modal class) = 55
f1 (frequency of the modal class) = 80
fo (frequency of the class preceding the modal class) = 45
f2 (frequency of the class succeeding the modal class) = 55
h (class size) = 2
Mode = l+(f1-fo/2f1-fo-f2) × h
= 5 + (80-45/2×80-45-55) × 2
= 5 + 35/60 × 2
= 5 + 35/60
= 6.2

19. The monthly income of 100 families are given as below :
 Income in Number of families 0-5000 8 5000 - 10000 26 10000 - 15000 41 15000 - 20000 16 20000 - 25000 3 25000 - 30000 3 30000 - 35000 2 35000 - 40000 1
Calculate the modal income .

Solution

The maximum class frequency is 41. The class corresponding to this frequency is 5-7.
So, the modal class is 10000-15000.
l (the lower limit of modal class) = 10000
f1 (frequency of the modal class) = 41
fo (frequency of the class preceding the modal class) = 26
f2 (frequency of the class succeeding the modal class) = 16
h (class size) = 5000
Mode = l+(f1-fo/2f1-fo-f2) × h
= 10000 + (41-26/2 × 41-26 - 16) × 5000
= 10000 + 15/40 × 5000
= 10000 +1875
= 11875