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.
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, xi = (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