Question

What is the standard deviation of the data set?
7,3,4, 2, 5, 6,9

Answer 1

2.4103

Explanation:

The first step in evaluating the sample standard deviation of a data set involves the determination of the sample mean.

The sample mean is simply the average value of the data set;

sample mean =
`(7+3+4+2+5+6+9)/(7)=5.1429`

The next step is to evaluate the sum of the squares of deviations from the mean;

sum of squares of deviation =
`(7-5.1429)^(2)+(3-5.1429)^(2)+(4-5.1429)^(2)+(2-5.1429)^(2)+(5-5.1429)^(2)+(6-5.1429)^(2)+(9-5.1429)^(2)=34.8571`

We then divide the sum of squares of deviation by (n-1) where n is the sample size to obtain the sample variance;

variance =
`(34.8571)/(7-1)=5.8095`

The standard deviation is simply the square-root of variance;

`√(5.8095)=2.4103`