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A doctor's office has a computer file showing the heights of 100 male patients of one of the doctors of the practice. the heights range from 18 inches to 68 inches. by accident, the greatest height has been recorded as 680 inches, instead of 68 inches. (a) does this affect the average? if so, by how much? (b) does this affect the median? if so by how much?

Answer :

The effect of the mistake is:

  • The mean value obtained is larger.
  • The median value is not affected.

The average value recorded is larger than it actually is. Hence , the average value is affected by the mistake. Given the information supplied, we can only deduce that the mean value will be greater than the actual average.

The mean involves taking the sum of all the values and dividing it by the number of values.

Using a value of 680 instead of 68 will mean that, the sum obtained is greater than the actual sum.

The median on the other hand isn't affected by this error, because, the arrangement of the values isn't changed.

The sorting of values is very crucial to calculating the Median. However, either 68 or 680. The position of the maximum value remains unchanged.

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Rewritten by : Barada

A) Yes. we don't have enough information so this can not be determined.
B) No, it would just be an outlier.