Question

Manually calculate the mean, median, mode, and range of the BMI values. Show all of your work.

BMI values 24.0, 21.2, 21.4, 25.1, 21.9, 31.1, 22.3, 29.2, 20.7, 23.3, 31.8, 20.7, 27.5, 25.9, 20.8, 28.3, 22.3, 25.7, 24.0, 26.9, 22.5, 20.2, 24.0, 29.5, 33.5

Answer 1

Solution

The sample mean is

Mean = (x / n) )

=24+21.2+21.4+25.1+21.9+31.1+22.3+29.2+20.7+23.3+31.8+20.7+27.5+25.9+20.8+28.3+22.3+25.7+24+26.9+22.5+20.2+24+29.5+33.525

=623.8/25

=24.952

Mean = =24.952

Median :
Observations in the ascending order are :
20.2,20.7,20.7,20.8,21.2,21.4,21.9,22.3,22.3,22.5,23.3,24,24,24,25.1,25.7,25.9,26.9,27.5,28.3,29.2,29.5,31.1,31.8,33.5

Here, n=25 is odd.

M= value of (n+12)th observation

= value of (25+12)th observation

= value of 13th observation

=24
Median =24

Mode :
In the given data, the observation 24 occurs maximum number of times (3)

∴Z=24

Mode =24

The range = Maximum value + Minimum value

= 33.5 + 20.2

= 13.3

The range = 13.3