Question

for the following set of data, find the sample standard deviation, to the nearest hundredth. 56, 24, 25, 47, 28, 26, 40

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{56 + 24+25+47+28+26+40}{7}=\frac{246}{7}\approx35.14$

Step2: Calculate the squared - differences

$(56 - 35.14)^2=(20.86)^2 = 435.14$
$(24 - 35.14)^2=(-11.14)^2 = 124.10$
$(25 - 35.14)^2=(-10.14)^2 = 102.82$
$(47 - 35.14)^2=(11.86)^2 = 140.66$
$(28 - 35.14)^2=(-7.14)^2 = 50.98$
$(26 - 35.14)^2=(-9.14)^2 = 83.54$
$(40 - 35.14)^2=(4.86)^2 = 23.62$

Step3: Calculate the sum of squared - differences

$S=\ 435.14+124.10+102.82+140.66+50.98+83.54+23.62 = 960.86$

Step4: Calculate the sample variance

The sample variance $s^{2}=\frac{S}{n - 1}=\frac{960.86}{7-1}=\frac{960.86}{6}\approx160.14$

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{160.14}\approx12.65$

Answer:

$12.65$