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 = [tex]\frac{7+3+4+2+5+6+9}{7}=5.1429[/tex]
The next step is to evaluate the sum of the squares of deviations from the mean;
sum of squares of deviation = [tex](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[/tex]
We then divide the sum of squares of deviation by (n-1) where n is the sample size to obtain the sample variance;
variance = [tex]\frac{34.8571}{7-1}=5.8095[/tex]
The standard deviation is simply the square-root of variance;
[tex]\sqrt{5.8095}=2.4103[/tex]
