Question

the data set below is the number of daily views over a week that a content creator received on a particular video they posted on the internet: 26, 8, 18, 23, 31, 19, 10 calculate the standard deviation of daily views. round your answer to the nearest tenth (one decimal place) if necessary.

Explanation:

Step1: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Here \(n = 6\), \(x=\{26,8,18,23,31,19,10\}\) (assuming it's a typo and there are 7 data - points, \(n = 7\)). \(\sum_{i=1}^{7}x_{i}=26 + 8+18+23+31+19+10=135\). \(\bar{x}=\frac{135}{7}\approx19.3\)

Step2: Calculate the variance

The formula for the variance \(s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}\).
\((26 - 19.3)^{2}=(6.7)^{2}=44.89\), \((8 - 19.3)^{2}=(- 11.3)^{2}=127.69\), \((18 - 19.3)^{2}=(-1.3)^{2}=1.69\), \((23 - 19.3)^{2}=(3.7)^{2}=13.69\), \((31 - 19.3)^{2}=(11.7)^{2}=136.89\), \((19 - 19.3)^{2}=(-0.3)^{2}=0.09\), \((10 - 19.3)^{2}=(-9.3)^{2}=86.49\)
\(\sum_{i = 1}^{7}(x_{i}-\bar{x})^{2}=44.89+127.69 + 1.69+13.69+136.89+0.09+86.49=411.03\)
\(s^{2}=\frac{411.03}{6}\approx68.5\)

Step3: Calculate the standard deviation

The formula for the standard deviation \(s=\sqrt{s^{2}}\). \(s=\sqrt{68.5}\approx8.3\)

Answer:

\(8.3\)