NCERT Solutions
Class 10 Maths
Statistics

Ex.13.2 Q.3
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.
It can be observed from the given data that the maximum class frequency is 40, belonging to (1500 – 2000) intervals.
Therefore, modal class = 1500 − 2000
Lower limit (l) of modal class = 1500
Frequency (f1) of modal class = 40
Frequency (f0) of class preceding modal class = 24
Frequency (f2) of class succeeding modal class = 33
Class size (h) = 500
Mode = l + {(f1 – f0) ÷ (2f1 – f0 – f2)} × h
= 1500 + {(40 - 24) ÷ (2 × 40 – 24 – 33)} × 500
= 1500 + {16 ÷ (80 - 57)} × 500
= 1500 + (8000 ÷ 23)
= 1500 + 347.826
= 1847.826
= 1847.83
Therefore, modal monthly expenditure was Rs 1847.83.
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 = 500
Taking 2750 as assured mean (a), di, ui, and fiui can be calculated as above.
From the table, it can be observed that
Σfi = 200
Σfiui = -35
Now, Mean = a + (Σfiui ÷ Σfi ) h
= 2750 + (-35 ÷ 200) × 500
= 2750 – (175 ÷ 2)
= 2750 – 87.5
= 2662.5
Therefore, mean monthly expenditure was Rs 2662.50.