Question

1. which measure of central tendency is most affected by extreme values?

a. median
b. range
c. mode
d. mean

Explanation:

• Median: It is the middle value when data is ordered. Extreme values do not affect it much as it only depends on the position of values.
• Range: It is a measure of dispersion (not a central - tendency measure).
• Mode: It is the most frequently occurring value. Extreme values do not change the mode unless the extreme value becomes the most frequent (which is rare in a data - set with a pre - existing mode).
• Mean: It is calculated as \(\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Extreme values (either very large or very small) can significantly pull the mean in the direction of the extreme value. For example, if we have data \(1,2,3,4,100\), the mean is \(\frac{1 + 2+3 + 4+100}{5}=\frac{110}{5} = 22\), while the median is \(3\).

Answer:

d. Mean