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# The following table shows the ages of the patients admitted in a hospital during a year:

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The following table shows the ages of the patients admitted in a hospital during a year:

Age (in years) - Number of patients

5 - 15             → 6

15 - 25          →  11

25 - 35          → 21

35 - 45          → 23

45 - 55        → 14

55 - 65        → 5

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

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To find out the modal class, let us the consider the class interval with high frequency

Here, the greatest frequency = 23, so the modal class = 35 – 45,

l = 35,

class width (h) = 10

fm = 23,

f1 = 21 and f2 = 14

The formula to find the mode is

Mode = l+ [(fm-f1)/(2fm-f1-f2)] × h

Substitute the values in the formula, we get

Mode = 35 + [(23 - 21)/(46 - 21 - 14)] × 10

Mode = 35 + (20/11) = 35+1.8

Mode = 36.8 year

So the mode of the given data = 36.8 year

Calculation of Mean:

First find the midpoint using the formula, x= (upper limit +lower limit)/2

The mean formula is

Mean = x̄ = ∑fixi /∑fi

= 2830/80

= 35.37 years

Therefore, the mean of the given data = 35.37 years

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