Which central measure is most affected by the outlier of this data set: 8, 10, 10, 11, 16, 17, 19, 21, 41?

Question

Mathematics

Beckham

3 September, 09:49

Which central measure is most affected by the outlier of this data set: 8, 10, 10, 11, 16, 17, 19, 21, 41?

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Answers (1)

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Gabrielle Monroe · Answer 1

The mean is the most affected.

Step-by-step explanation:

In statistics, central measures are the mean, the median and mode.

The mean is the average, it indicates the value that the majority of the data set is falling to.

The median is the central value, literally. The value placed in the middle of the data set is the median.

The mode is the value with the highest frequency. In other words, the value that repeats the most.

So, in the given data set, the outlier is 41, which is a drastically greater value than the other ones in the data set. However, this oulier doesn't affect the mode or the median, because you can replace it with 22, and you would have the same median and the same mode.

Therefore, the central measure most affected is the mean, because this statistic measure uses all values in the data set, so if we change the outlier, the mean would change too.

So, the right answer is the mean.