Question

the bowling scores for six people are: 27, 142, 145, 146, 154, 162 what is the most appropriate measure of center? a. the range b. the standard deviation c. the median d. the mean

Explanation:

Step1: Analyze the data set

The data set is \(27, 142, 145, 146, 154, 162\). There is an out - lier (\(27\)).

Step2: Recall the properties of measures of center

• The mean (\(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\)) is affected by outliers. For this data set, the outlier \(27\) will pull the mean down.
• The median: For a set of \(n = 6\) (even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered values. Here, the \(\frac{6}{2}=3\)rd value is \(145\) and the \((\frac{6}{2}+1) = 4\)th value is \(146\). The median \(M=\frac{145 + 146}{2}=145.5\). The median is not affected by outliers as much as the mean.
• The range (\(R=\text{Max}-\text{Min}\)) and standard deviation (\(\sigma=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\mu)^{2}}{n}}\)) are measures of spread, not of center.

So, the most appropriate measure of center is the median.

Answer:

C. The median