Question

which statements are true about the median of a data set? check all that apply.
□ the median isn’t affected much by one outlier.
□ the median is always affected by one outlier.
□ the median is the number in the middle on an ordered set of data.
□ to find the median, find the difference between the highest and lowest numbers.
□ to find the median of an even data set, find the average of the two middle numbers.

Explanation:

• The median is the middle number in an ordered set of data. For an even - numbered data set, the median is the average of the two middle numbers.
• The median is not as affected by outliers as the mean. For example, if we have a data set \(1,2,3,4,100\), the ordered set is \(1,2,3,4,100\). The median is \(3\) (the middle number when \(n = 5\), for \(n=4\) like \(1,2,4,100\), the median is \(\frac{2 + 4}{2}=3\)), while the mean is more affected by the outlier \(100\).

• The statement "To find the median, find the difference between the highest and lowest numbers" is incorrect. The difference between the highest and lowest numbers is the range.
• The statement "The median is always affected by one outlier" is incorrect. As shown in the examples above, the median is relatively resistant to outliers.

Answer:

• The median isn't affected much by one outlier.
• The median is the number in the middle on an ordered set of data.
• To find the median of an even data set, find the average of the two middle numbers.