A data set has 10 distinct positive whole numbers, all of which are less than or

Question

A data set has 10 distinct positive whole numbers, all of which are less than or equal to 20 except for one whose value is 220. Which of the following must be true?

1) The mean is less than or equal to 30.

2) The mean is less than or equal to 40.

3) The mean is a whole number.

4) The median is a whole number.

5) The median is not a whole number.

6) The mean is not a whole number.

7) The range of the data (difference between the maximum and minimum values) is less than 200.

8) The median is less than the mean.

Explanation / Answer

Since 9 values are less than equal to 20 so sum of these 9 values must be less than or equal to 20*9 =180. So sum of 10 values must be less than equal to 400. That is average must be less than or equal to (400/10) = 40.

so option (2) is correct.

We can't say that mean or median will be whole number. Median will be average of 5th and 6th data value of the ordered data set. So it may be possible that mean and median will be whole number or not a whole number.

Since except maximum value all the values are less than equal to 20 so range will be greater than or equal to 200.

yes, median will be less than mean because data has an high outlier (220). So option (8) is also true.

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