Question

what are outliers? describe the effects of outliers on the mean, median, and mode

choose the correct answer below

a. an outlier in a data set is a value that is much higher or much lower than almost all other values. an outlier does not change the mean, median, or mode of a data set

b. an outlier in a data set is a value that is much higher or much lower than almost all other values. an outlier can change the mean of a data set, but does not affect the median or mode

c. an outlier in a data set is a value that is much higher than almost all other values. an outlier can change the median of a data set, but does not affect the mean or mode

d. an outlier in a data set is a value that is much higher than almost all other values. an outlier can change the mode of a data set, but does not affect the mean or median

Explanation:

1. First, recall the definition of an outlier: an outlier is a value much higher or lower than most other values (not just higher). So options C and D, which define outliers as only much higher, are incorrect.
2. Then, analyze the effect on mean, median, and mode:

• Mean: Since mean is the sum of values divided by the number of values, an outlier (very high or low) will change the sum, thus changing the mean.
• Median: The median is the middle value (or average of two middle values). An outlier, being at the extreme, does not change the middle position of the data (unless the data set is very small, but generally, it has little effect on the median).
• Mode: The mode is the most frequent value. An outlier, being a rare extreme value, does not affect the frequency of the most common value.
• Option A says an outlier does not change mean, median, or mode, which is wrong because mean is affected. Option B correctly defines an outlier and states it affects the mean but not median or mode.

Answer:

B. An outlier in a data set is a value that is much higher or much lower than almost all other values. An outlier can change the mean of a data set, but does not affect the median or mode