Question

the number of hits that a web site receives in 10 days is as follows: 45, 48, 25, 37, 40, 32, 25, 41, 38, 29 find the standard deviation for this data. 6.6 7.6 8.0 64.0

Explanation:

Step1: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\).
Here \(n = 10\), \(x=\{45,48,25,37,40,32,25,41,38,29\}\)
\(\sum_{i=1}^{10}x_{i}=45 + 48+25+37+40+32+25+41+38+29=360\)
\(\bar{x}=\frac{360}{10}=36\)

Step2: Calculate the variance

The formula for the variance \(s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}\)
\((x_{1}-\bar{x})^{2}=(45 - 36)^{2}=81\)
\((x_{2}-\bar{x})^{2}=(48 - 36)^{2}=144\)
\((x_{3}-\bar{x})^{2}=(25 - 36)^{2}=121\)
\((x_{4}-\bar{x})^{2}=(37 - 36)^{2}=1\)
\((x_{5}-\bar{x})^{2}=(40 - 36)^{2}=16\)
\((x_{6}-\bar{x})^{2}=(32 - 36)^{2}=16\)
\((x_{7}-\bar{x})^{2}=(25 - 36)^{2}=121\)
\((x_{8}-\bar{x})^{2}=(41 - 36)^{2}=25\)
\((x_{9}-\bar{x})^{2}=(38 - 36)^{2}=4\)
\((x_{10}-\bar{x})^{2}=(29 - 36)^{2}=49\)
\(\sum_{i = 1}^{10}(x_{i}-\bar{x})^{2}=81+144 + 121+1+16+16+121+25+4+49=578\)
\(s^{2}=\frac{578}{9}\approx64.22\)

Step3: Calculate the standard deviation

The formula for the standard deviation \(s=\sqrt{s^{2}}\)
\(s=\sqrt{\frac{578}{9}}\approx\sqrt{64.22}\approx8.0\)

Answer:

8.0