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

Answer - 1 : -

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

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.

Answer - 2 : -

We see that frequency of 40 is maximum which is 41
∴Mode =40

Question - 3 : - Find the mode of the following distribution.

Answer - 3 : -

Question - 4 : - Compare the modal ages of two groups of students appearing for an entrance test :

Answer - 4 : -

(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.

Answer - 5 : -

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.

Answer - 6 : - Writing the classes in exclusive form,

Here model class is 165.5 – 168.5
and l = 165.5, h = 3, f= 142, f₁= 118, f₂= 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.

Answer - 7 : -

(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.

Answer - 8 : -

We see that class 60-80 has the maximum frequency 61
∴ It is the modal class
Here l = 60, f= 6, f₁ = 52, f₂ = 38,h = 20
∴ Modal of life time (inhrs.)

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)

Answer - 9 : -

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:

Answer - 10 : - Let assumed mean (A) = 32.5

(i) We see that the class30-35 has the maximum frequency
∴ It is the modal class
Here l = 30,f = 10, f₁ = 9, f₂ = 3, h = 5

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