Question

which measure of central tendency is most affected by outliers?
a. median
b. all of the answers
c. mode
d. mean

Explanation:

• Mean: The mean is calculated by summing all values and dividing by the number of values. An outlier (a very large or very small value) will significantly affect the sum, thus changing the mean. For example, if we have data \(1,2,3,4\), mean is \(\frac{1 + 2+3 + 4}{4}=\frac{10}{4} = 2.5\). If we add an outlier \(100\), new mean is \(\frac{1+2 + 3+4+100}{5}=\frac{110}{5}=22\).
• Median: The median is the middle - value when data is ordered. For example, for data \(1,2,3,4\), median is \(\frac{2 + 3}{2}=2.5\). For data \(1,2,3,4,100\), median is \(3\). The change is not as drastic as for the mean.
• Mode: The mode is the most frequently occurring value. An outlier usually does not affect the mode at all. For example, if data is \(1,2,2,3,4\) (mode is \(2\)), adding an outlier \(100\) (data \(1,2,2,3,4,100\)) still has mode \(2\).

Answer:

d. Mean