NCERT Solutions
Class 10 Maths
Statistics

Ex.13.2 Q.1
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.
To find the class mark (xi) for each interval, the following relation is used.
Class mark xi = (Upper limit + Lower limit) ÷ 2
Taking 30 as assured mean (a), di and fidi can be calculated as follows.
From the table, it can be observed that
Σfi = 80
Σfidi = 430
Now, Mean = a + (Σfidi ÷ Σfi )
= 30 + (430 ÷ 80)
= 30 + 5.375
= 35.375
= 35.38
Mean of this data is 35.38. It represents that on an average,
the age of a patient admitted to hospital was 35.38 years.
It can be observed that the
maximum class frequency is 23 belonging to class interval 35 − 45.
Modal class = 35 − 45
Lower limit (l) of modal class = 35
Frequency (f1) of modal class = 23
Class size (h) = 10
Frequency (f0) of class preceding the modal class = 21
Frequency (f2) of class succeeding the modal class = 14
Mode = l + {(f1 – f0) ÷ (2f1 – f0 – f2)} × h
= 35 + {(23 - 21) ÷ (2 × 23 – 21 – 14)} × 10
= 35 + {2 ÷ (46 - 35)} × 10
= 35 + (20 ÷ 11)
= 35 + 1.81
= 36.8
Mode is 36.8. It represents that the age of maximum number of patients admitted in hospital was 36.8 years.