Question

question for the following set of data, find the population standard deviation, to the nearest hundredth. 53, 75, 123, 103, 87, 51, 134 answer attempt 1 out of 2 open statistics calculator copy values for calculator submit answer watch video show examples

Explanation:

Step1: Calculate the mean

The data set is \(53,75,123,103,87,51,134\). The mean \(\bar{x}=\frac{53 + 75+123+103+87+51+134}{7}=\frac{626}{7}\approx89.43\)

Step2: Calculate the squared - differences

\((53 - 89.43)^2=(- 36.43)^2 = 1327.14\)
\((75 - 89.43)^2=(-14.43)^2 = 208.22\)
\((123 - 89.43)^2=(33.57)^2 = 1126.94\)
\((103 - 89.43)^2=(13.57)^2 = 184.14\)
\((87 - 89.43)^2=(-2.43)^2 = 5.9\)
\((51 - 89.43)^2=(-38.43)^2 = 1476.86\)
\((134 - 89.43)^2=(44.57)^2 = 1986.48\)

Step3: Calculate the variance

The variance \(\sigma^{2}=\frac{1327.14 + 208.22+1126.94+184.14+5.9+1476.86+1986.48}{7}=\frac{6315.7}{7}\approx902.24\)

Step4: Calculate the standard deviation

The standard deviation \(\sigma=\sqrt{902.24}\approx30.04\)

Answer:

\(30.04\)