Question

The following distribution gives the state-wise teachers-students ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures:
Number of students per teacher Number of states/UT
15 – 20 3
20 – 25 8
25 – 30 9
30 – 35 10
Number of students per teacher Number of states/UT
35 – 40 3
40 – 45 0
45 – 50 0
50 – 55 2

Answer 1

SOLUTION :  

Mode = l + (f1-f0/2f1-f0-f2) ×h

l = lower limit of the modal class

h = size of the class intervals

f1 = frequency of the modal class

f0 = frequency of the class preceding the modal class

f2 = frequency of the class succeed in the modal class.

FREQUENCY DISTRIBUTION TABLE is in the attachment  

Here the maximum frequency is 10, and the class corresponding to this frequency is 30 – 35. So the modal class is 30 – 35.

Therefore,l = 30 , h = 35 – 30 = 5,  f1= 10,  f0= 9 , f2 = 3

Mode = l + [(f1- f0) / (2f1- f0 - f2)] ×h

= 30 + [(10 - 9)/(2 × 10 - 9 – 3) ]×5

= 30 +[(1 × 5)/(20 - 12)]

= 30 + [5/8]

= 30 + 0.625

= 30.625 hours

Hence, the mode is 30.6 .

From the table : Σfi = 35 , Σfixi = 1022.5

Mean = Σfixi /Σfi

Mean = 1022.5/35 = 29.2  

Hence, the mean of the data is 29.2

The mode of the number of students per teacher in the state is more than the mean of the number of students per teacher in the states.

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Mode group of the table = (30 - 35)
l = 30, f1 = 10, f0 = 3, f2 = 9, h = 5

Mode = l + (f1 - f0 / 2f1 - f0 - f2) × h
=30 + (10 - 9 / 2×10 - 3 - 9) × 5
=30 + (1 / 20 - 12) × 5
=30 + (1 / 8) × 5
=30 + 5/8
=30 + 0.62
=34.62

Mean = fixi / fi
= 1022.5 / 35
= 29.2

Hope it helps you✌️✌️