NCERT Solutions
Class 10 Maths
Statistics
Ex.13.2 Q.4
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.
It can be observed from the given data that the maximum class frequency is 10 belonging to class interval 30 − 35.
Therefore, modal class = 30 − 35
Class size (h) = 5
Lower limit (l) of modal class = 30
Frequency (f1) of modal class = 10
Frequency (f0) of class preceding modal class = 9
Frequency (f2) of class succeeding modal class = 3
Mode = l + {(f1 – f0) ÷ (2f1 – f0 – f2)} × h
= 30 + {(10 - 9) ÷ (2 × 10 – 9 – 3)} × 5
= 30 + (1 ÷ (20 - 12) × 5)
= 30 + (5 ÷ 8)
= 30 + 0.625
= 30.625
= 30.6
It represents that most of the states or U.T. have a teacher-student ratio as 30.6.
To find the class mark (xi) for each interval, the following relation is used.
Class mark xi = (Upper limit + Lower limit) ÷ 2
Class size (h) of this data = 5
Taking 32.5 as assured mean (a), di, ui, and fiui can be calculated as above.
From the table, it can be observed that
Σfi = 35
Σfiui = -32
Now, Mean = a + (Σfiui ÷ Σfi ) × h
= 32.5 + (-23 ÷ 35) × 5
= 32.5 – 
= 32.5 – 3.28
= 29.22
Therefore, mean of the data is 29.2.
It represents that on an average, teacher−student ratio was 29.2.