Question

question for the following set of data, find the sample standard deviation, to the nearest hundredth. 135, 187, 154, 108, 153, 176, 154, 174

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{135 + 187+154+108+153+176+154+174}{8}=\frac{1241}{8}=155.125$

Step2: Calculate the squared - differences

$(135 - 155.125)^2=(-20.125)^2 = 405.015625$
$(187 - 155.125)^2=(31.875)^2=1016.015625$
$(154 - 155.125)^2=(-1.125)^2 = 1.265625$
$(108 - 155.125)^2=(-47.125)^2=2220.765625$
$(153 - 155.125)^2=(-2.125)^2 = 4.515625$
$(176 - 155.125)^2=(20.875)^2=435.765625$
$(154 - 155.125)^2=(-1.125)^2 = 1.265625$
$(174 - 155.125)^2=(18.875)^2=356.265625$

Step3: Sum the squared - differences

$S=405.015625+1016.015625 + 1.265625+2220.765625+4.515625+435.765625+1.265625+356.265625=4440.875$

Step4: Calculate the sample variance

The sample variance $s^2=\frac{S}{n - 1}=\frac{4440.875}{8 - 1}=\frac{4440.875}{7}\approx634.410714$

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{s^2}=\sqrt{634.410714}\approx25.19$

Answer:

$25.19$