question #6\nfind the standard deviation of a group of men whose height in centimeters is given below.\nmens…

Explanation:

Step1: Calculate the mean

Let the data - set be (x_1,x_2,\cdots,x_n). Here (n = 18), and (\sum_{i = 1}^{18}x_i=178 + 175+176+173+171+178+178+173+184+169+179+180+173+177+179) (\sum_{i = 1}^{18}x_i = 3150) The mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}=\frac{3150}{18}=175)

Step2: Calculate the squared - differences

For each data - point (x_i), calculate ((x_i-\bar{x})^2). For example, when (x_1 = 178), ((x_1-\bar{x})^2=(178 - 175)^2=9).

Step3: Calculate the variance

The variance (s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}) (\sum_{i = 1}^{18}(x_i - 175)^2=(178 - 175)^2+(175 - 175)^2+(176 - 175)^2+(173 - 175)^2+(171 - 175)^2+(178 - 175)^2+(178 - 175)^2+(173 - 175)^2+(184 - 175)^2+(169 - 175)^2+(179 - 175)^2+(180 - 175)^2+(173 - 175)^2+(177 - 175)^2+(179 - 175)^2) (\sum_{i = 1}^{18}(x_i - 175)^2=9 + 0+1 + 4+16+9+9+4+81+36+16+25+4+4+16) (\sum_{i = 1}^{18}(x_i - 175)^2=274) The variance (s^2=\frac{274}{18 - 1}=\frac{274}{17}\approx16.1176)

Step4: Calculate the standard deviation

The standard deviation (s=\sqrt{s^2}=\sqrt{\frac{274}{17}}\approx4.0147\approx4.08)

Answer:

4.08