Question

the ages of a sample of canadian tourists flying from toronto to hong kong were 28, 22, 69, 52, 53, 26, 79, 55, 43, and 38. note: round the range to nearest whole number and the standard deviation to 2 decimal places. required: a. compute the range. b. compute the standard deviation.

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