Question

Consider a data set with five different data values. Suppose the highest value is increased by 10 and the lowest is decreased by 10. (If this question seems confusing because you aren't given any data, make up your own five data values, and then add 10 to the largest one, and subtract 10 from the smallest one.) (a) How does the mean change? The mean decreases because the minimum value decreased by 10. The mean does not change, because the sum of the data does not change.     The mean increases because the two new values are further away from the rest of the data than they were before. The mean increases because the sum of the data increases. (b) How does the median change? The median increases because the data has more extreme values. The median does not change. Changing the minimum and maximum data values does not affect the median.     The median decreases because the minimum value decreased by 10. The median changes because the sum of the data changes. The median increases because it is affected by changes to the minimum and maximum values. Again, consider the data set with five different data values. Suppose the highest value is increased by 10 and the lowest is left unchanged. (If this question seems confusing because you aren't given any data, make up your own five data values, and then add 10 to the largest one, and make no change to the smallest one.) (c) How does the mean change? The mean increases because the sum of the data increases. The mean does not change, because the sum of the data does not change.     The mean decreases because the minimum value decreased. The mean increases because the two new values are further away from the rest of the data than they were before. (d) How does the median change? The median increases because the sum of the data changes. The median decreases because the minimum value decreased.     The median decreases because most of the data is much lower than the maximum value. The median does not change. Changing the maximum data value does not affect the median. The median increases because it is affected by changes to the minimum and maximum values.

Answer 1

**(a)** The mean **increases**.

**(b)** The median **does not change**.

**(c)** The mean **increases**.

**(d)** The median **does not change**.

Explanation:

The answers to the questions are as follows:

**(a)** The mean increases because the sum of the data increases.

**(b)** The median does not change. Changing the minimum and maximum data values does not affect the median.

**(c)** The mean increases because the sum of the data increases.

**(d)** The median does not change. Changing the maximum data value does not affect the median.

Here's the explanation for each answer:

**(a)** When we increase the highest value by 10 and decrease the lowest value by 10, the sum of the data increases. The mean is calculated by dividing the sum of the data by the number of data values, so the mean will also increase.

**(b)** The median is the middle value in a sorted data set. When we increase the highest value by 10 and decrease the lowest value by 10, the middle value in the data set does not change. Therefore, the median does not change.

**(c)** When we increase the highest value by 10, the sum of the data increases. The mean is calculated by dividing the sum of the data by the number of data values, so the mean will also increase.

**(d)** The median is the middle value in a sorted data set. When we increase the highest value by 10, the middle value in the data set does not change. Therefore, the median does not change.

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