the ages of a sample of canadian tourists flying from toronto to hong kong were 28, 22, 69, 52, 53, 26, 79…

Explanation:

Step1: Find maximum and minimum values

The data set is (28, 22, 69, 52, 53, 26, 79, 55, 43, 38). The maximum value (x_{max}=79) and the minimum value (x_{min}=22).

Step2: Calculate the range

The formula for the range (R) is (R = x_{max}-x_{min}). So (R=79 - 22=57).

Step3: Calculate the mean

The mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}), where (n = 10) and (\sum_{i=1}^{10}x_{i}=28 + 22+69+52+53+26+79+55+43+38=465). Then (\bar{x}=\frac{465}{10}=46.5).

Step4: Calculate the squared - differences

For each data point (x_i), calculate ((x_i-\bar{x})^2). For example, for (x_1 = 28), ((28 - 46.5)^2=(-18.5)^2 = 342.25). Do this for all data points and sum them up: (\sum_{i = 1}^{n}(x_i-\bar{x})^2=(28 - 46.5)^2+(22-46.5)^2+(69 - 46.5)^2+(52-46.5)^2+(53 - 46.5)^2+(26-46.5)^2+(79-46.5)^2+(55 - 46.5)^2+(43-46.5)^2+(38-46.5)^2) (=342.25+590.25 + 506.25+30.25+42.25+420.25+1056.25+72.25+12.25+72.25 = 3144.5)

Step5: Calculate the standard deviation

The formula for the sample standard deviation (s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}). Here (n=10), so (s=\sqrt{\frac{3144.5}{9}}\approx\sqrt{349.3889}\approx18.69)

Answer:

a. 57 b. 18.69