Question 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.

Answer:

To find the class marks (x_i), the following relation is used.

Taking 30 as assumed mean (a), d_i and f_id_i are calculated as follows.

From the table, we obtain

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 is 36.8. It represents that the age of maximum number of patients admitted in hospital was 36.8 years.

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