Video: Understanding the Effect of an Outlying Value on the Standard Deviation of a Data Set

The data set shown contains a potentially outlying value of 32. What effect would removing this have on the calculation of the standard deviation? [A] the standard deviation would not change. [B] The standard deviation would decrease. [C] The standard deviation would increase.

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Video Transcript

The data set shown contains a potentially outlying value of 32. What effect would removing this have on the calculation of the standard deviation? Would it be a) the standard deviation would not change, b) the standard deviation would decrease, or c) the standard deviation would increase?

Standard deviation is a measure that is used to quantify the amount of variation of a set of values. In basic terms, the greater the spread of numbers, the greater the standard deviation.

In this question, we are asked to consider the impact of removing 32 from the data set. 32 is a potential outlier. Any outlier can raise the standard deviation. This is because it will be further away from the mean than the other values.

As the potential outlier will increase the standard deviation, removing it would decrease the standard deviation. This means that the data set without the number 32 would have a lower standard deviation.

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