Questions
The following table shows the ages of the patients admitted to a hospital during a year:
Age (in years) | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 |
Number of patients | 6 | 11 | 21 | 23 | 14 | 5 |
Find the mode and the mean of the data given above. Compare and interpret the two
measures of central tendency.
detailed solution
1
For the modal class, let us the consider the class interval with highest 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+ []×h
Substitute the values in the formula, we get
Mode = 35+[]×10
Mode = 35+() = 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 =
Class Interval | Frequency (fi) | Mid-point (xi) | fixi |
5-15 | 6 | 10 | 60 |
15-25 | 11 | 20 | 220 |
25-35 | 21 | 30 | 630 |
35-45 | 23 | 40 | 920 |
45-55 | 14 | 50 | 700 |
55-65 | 5 | 60 | 300 |
Sum fi = 80 | Sum fixi = 2830 |
The mean formula is
Mean = x̄ =
=
= 35.37 years
Therefore, the mean of the given data = 35.37 years
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