Question

1. keisha gathered data by asking ten people the question, “how many indoor pets do you have?”. her results were 3, 12, 1, 0, 0, 2, 3, 0, 2, 1. which measure of center (mean or median) would best represent her data? explain your choice.

Explanation:

Step1: Sort the data

Sort the data set \(3, 12, 1, 0, 0, 2, 3, 0, 2, 1\) in ascending order: \(0,0,0,1,1,2,2,3,3,12\)

Step2: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Here \(n = 10\) and \(\sum_{i=1}^{10}x_{i}=0 + 0+0 + 1+1+2+2+3+3+12=24\). So the mean \(\bar{x}=\frac{24}{10}=2.4\)

Step3: Calculate the median

Since \(n = 10\) (even), the median \(M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}\). \(x_{5}=1\) and \(x_{6}=2\). So the median \(M=\frac{1 + 2}{2}=1.5\)

Step4: Analyze the effect of the outlier

The value \(12\) is an outlier. The mean is affected by outliers. The median is less affected by outliers.

Answer:

The median would best represent her data. The value \(12\) is an outlier. The mean (\(2.4\)) is pulled up by the outlier \(12\). The median (\(1.5\)) is less affected by the outlier and gives a better representation of the central - tendency of the data set \(0,0,0,1,1,2,2,3,3,12\)