Question

question: for the following set of data, find the population standard - deviation, to the nearest hundredth. 21, 38, 35, 22, 38, 36, 18, 21, 24 answer attempt 1 out of 2 open statistics calculator copy values for calculator watch video show examples

Explanation:

Step1: Calculate the mean

The data set is \(21,38,35,22,38,36,18,21,24\). The mean \(\mu=\frac{21 + 38+35+22+38+36+18+21+24}{9}=\frac{253}{9}\approx28.11\)

Step2: Calculate the squared - differences

For \(x_1 = 21\), \((x_1-\mu)^2=(21 - 28.11)^2=(-7.11)^2 = 50.5521\)
For \(x_2 = 38\), \((x_2-\mu)^2=(38 - 28.11)^2=(9.89)^2 = 97.8121\)
For \(x_3 = 35\), \((x_3-\mu)^2=(35 - 28.11)^2=(6.89)^2 = 47.4721\)
For \(x_4 = 22\), \((x_4-\mu)^2=(22 - 28.11)^2=(-6.11)^2 = 37.3321\)
For \(x_5 = 38\), \((x_5-\mu)^2=(38 - 28.11)^2=(9.89)^2 = 97.8121\)
For \(x_6 = 36\), \((x_6-\mu)^2=(36 - 28.11)^2=(7.89)^2 = 62.2521\)
For \(x_7 = 18\), \((x_7-\mu)^2=(18 - 28.11)^2=(-10.11)^2 = 102.2121\)
For \(x_8 = 21\), \((x_8-\mu)^2=(21 - 28.11)^2=(-7.11)^2 = 50.5521\)
For \(x_9 = 24\), \((x_9-\mu)^2=(24 - 28.11)^2=(-4.11)^2 = 16.8921\)

Step3: Calculate the variance

The population variance \(\sigma^{2}=\frac{\sum_{i = 1}^{n}(x_i-\mu)^2}{n}\)
\(\sum_{i = 1}^{9}(x_i-\mu)^2=50.5521+97.8121 + 47.4721+37.3321+97.8121+62.2521+102.2121+50.5521+16.8921 = 562.88\)
\(\sigma^{2}=\frac{562.88}{9}\approx62.54\)

Step4: Calculate the standard deviation

The population standard deviation \(\sigma=\sqrt{\sigma^{2}}=\sqrt{62.54}\approx7.91\)

Answer:

\(7.91\)