Meaures of Center Location and Variability

Question

The table below gives the number of hours spent watching TV last week by a sample of 24 children.

85	82	25	79	64	80
20	38	80	58	63	64
75	30	25	79	73	72
53	36	57	68	95	19

Find the standard deviation

Answer 1

It helps to have a calculator with a memory. Do not round until the end of your calculation.

There are n=24 values.

First, find the mean (arithmetic average) by adding up all 24 values and dividing by 24. Mean=(85+20+75+53+82+ ... + 72+19)/24 = 1420/24=59.1666...

Next, subtract the mean you just calculated from each individual value, square the difference and add them up. That is, (85-59.17)^2 + (20-59.17)^2 + (75-59.17)^2 + ... + (19-59.17)^2 = 12,235.3333...

Finally, divide the sum of the sqaured differences by n-1=23 and take the sqaure root for the SAMPLE standard deviation, resulting in sqrt(12,235.3333/23)=23.06 to 2 decimal places.