Question

A study of physical fitness tests for 12 randomly selected Pre-Medical students measured their exercise capacity (in minutes). The following data resulted:

34 19 33 30 43 36

32 41 31 31 37 18

Find the standard deviation  and the variance  for the sample data of the students' exercise capacity. Round to the nearest tenth.

Answer 1

Solution:

The formula for variance and standard deviation are given as below:

Sample variance = ∑(X - mean)^2/(n – 1)

Sample standard deviation = Sqrt[∑(X - mean)^2/(n – 1)]

Mean = ∑X/n

The required calculation table is given as below:

No.	X	(X - mean)^2
1	34	3.673623889
2	19	171.1735239
3	33	0.840283889
4	30	4.340263889
5	43	119.1736839
6	36	15.34030389
7	32	0.006943889
8	41	79.50700389
9	31	1.173603889
10	31	1.173603889
11	37	24.17364389
12	18	198.3401839
Total	385	618.9166667

Mean = 385/12 = 32.08333

Sample variance = ∑(X - mean)^2/(n – 1)

Sample variance = 618.9166667/(12 – 1) = 618.9166667/11 = 56.26515152

Sample variance = 56.3

Sample standard deviation = Sqrt(56.26515152)

Sample standard deviation = 7.501010033

Sample standard deviation = 7.5