## RD Sharma class 10 Solutions Chapter 7 Statistics Ex 7.5

### RD Sharma Class 10 Solutions Statistics Exercise 7.5

Question 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:

We see that 5 occurs in maximum times which is 5

∴ Mode = 5

we see that 3 occurs in maximum times i.e. 5

∴ Mode = 3

Here we see that 15 occurs in maximum times i.e. 54

∴ Mode = 15

Question 2.

The shirt sizes worn by a group of 200 persons, who bought the shirt from a store, are as follows :

Find the model shirt size worn by the group.

Solution:

We see that frequency of 40 is maximum which is 41

∴Mode = 40

Question 3.

Find the mode of the following distribution.

Solution:

Question 4.

Compare the modal ages of two groups of students appearing for an entrance test :

Solution:

(i) For group A

We see that class 18-20 has the maximum frequency

∴ It is a modal class

(ii) For group B

We see that class 18-20 has the maximum frequency

∴ It is a modal class

Question 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.

Solution:

We see that class 50-60 has the maximum frequency 20

∴ It is a modal class

Question 6.

The following is the distribution of height of students of a certain class in a certain city :

Find the average height of maximum number of students.

Solution:

Writing the classes in exclusive form,

Here model class is 165.5 – 168.5

and l = 165.5, h = 3, f= 142, f_{1}= 118, f_{2}= 127

Question 7.

The following table shows the ages of the patients admitted in a hospital during a year :

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Solution:

(i) We see that class 35-45 has the maximum frequency 23

∴ It is a modal class

= 35.375 = 35.37 years

We see that mean is less than its mode

Question 8.

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components :

Determine the modal lifetimes of the components.

Solution:

We see that class 60-80 has the maximum frequency 61

∴ It is the modal class

Here l = 60, f= 6, f_{1} = 52, f_{2} = 38,h = 20

∴ Modal of life time (in hrs.)

Question 9.

The following table gives the daily income of 50 workers of a factory :

Find the mean, mode and median of the above data. (C.B.S.E. 2009)

Solution:

Here i = 20 and AM = 150

(ii) Max frequency = 14

∴ Model class = 120 – 140

Question 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:

Let assumed mean (A) = 32.5

(i) We see that the class 30-35 has the maximum frequency

∴ It is the modal class

Here l = 30,f = 10, f_{1} = 9, f_{2} = 3, h = 5

Question 11.

Find the mean, median and mode of the following data:

Solution:

Let assumed mean (A) =175

(i) Here N = 25, [latex]\frac { 5 }{ 3 }[/latex] = [latex]\frac { 25 }{ 2 }[/latex] = 12.5 or 13 which lies in the class 150-200

l= 150, F= 10, f= 6, h = 50

Question 12.

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data.

Solution:

We see that class 40-50 has the maximum frequency

∴ It is a modal class

Question 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:

Solution:

Let assumed mean (A) = 135

Here N = 68 , [latex]\frac { N }{ 2 }[/latex] = [latex]\frac { 68 }{ 2 }[/latex] = 34

Question 14.

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, And the modal size of the surnames.

Solution:

Let Assumed mean (A) = 8.5

(i) Here N = 100, [latex]\frac { N }{ 2 }[/latex] = [latex]\frac { 100 }{ 2 }[/latex] = 50 which lies in the class 7-10

Here l = 7, F = 36, f= 40, h = 3

Question 15.

Find the mean, median and mode of the following data (C.B.S.E. 2008)

Solution:

Let assumed mean A = 70

(i) Here N = 50, then [latex]\frac { N }{ 2 }[/latex] = [latex]\frac { 50 }{ 2 }[/latex] = 25 which lies in the class 60-80

∴ l= 60, F= 24, f = 12 , h = 20

Question 16.

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

Solution:

(i) We see that the c ass 1500-2000 has maximum frequency 40

∴ It is a modal class

Here l = 1500, f = 40 , f_{1} = 24 , f_{2} = 33 , h =500

Question 17.

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

Find the mode of the data.

Solution:

We see that class 4000-5000 has the maximum frequency 18

∴It is a modal class

Question 18.

The frequency distribution table of agriculture holdings in a village is given below:

Find the modal agriculture holdings of the village.

Solution:

Here the maximum class frequency is 80,

and the class corresponding to this frequency is 5-7.

So, the modal class is 5-7.

l (lower limit of modal class) = 5

f_{1} (frequency of the modal class) = 80

f_{0} (frequency of the class preceding the modal class) = 45

f_{2}(frequency of the class succeeding the modal class) = 55

h (class size) = 2

Hence, the modal agricultural holdings of the village is 6.2 hectares.

Question 19.

The monthly income of 100 families are given as below:

Solution:

In a given data, the highest frequency is 41, which lies in the interval 10000-15000.

Here, l = 10000,f_{1} = 41, f_{0} = 26,f_{2} = 16 and h = 5000

### RD Sharma class 10 Solutions Chapter 7 Statistics Ex 7.5