Question

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

Answer 1

Answer:

2.4103

Step-by-step 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 = $\frac{7+3+4+2+5+6+9}{7}=5.1429$

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 = $\frac{34.8571}{7-1}=5.8095$

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

$\sqrt{5.8095}=2.4103$