Consider a data set with at least three data values. Suppose the highest value is increased by 10 and the lowest is decreased by 10.(a) Does the mean change? Explain.No, the sum of the data does not change.Yes, the number of data values changes. No, the number of data values does not change.Yes, changing the extreme data values affects the mean.Yes, the sum of the data changes.(b) Does the median change? Explain.Yes, the sum of the data changes.No, changing the extreme data values does not affect the median. Yes, the number of data values changes.No, the sum of the data does not change.No, the number of data values does not change.(c) Is it possible for the mode to change? Explain.Yes, depending on the range of the data values.No, all values will still occur at the same frequency. Yes, depending on which data value occurs most frequently after the data are changed.No, the only change is an increased frequency of 1 for the extreme values.Yes, depending on the number a data values.
Question
Consider a data set with at least three data values. Suppose the highest value is increased by 10 and the lowest is decreased by 10.(a) Does the mean change? Explain.No, the sum of the data does not change.Yes, the number of data values changes. No, the number of data values does not change.Yes, changing the extreme data values affects the mean.Yes, the sum of the data changes.(b) Does the median change? Explain.Yes, the sum of the data changes.No, changing the extreme data values does not affect the median. Yes, the number of data values changes.No, the sum of the data does not change.No, the number of data values does not change.(c) Is it possible for the mode to change? Explain.Yes, depending on the range of the data values.No, all values will still occur at the same frequency. Yes, depending on which data value occurs most frequently after the data are changed.No, the only change is an increased frequency of 1 for the extreme values.Yes, depending on the number a data values.
Solution
(a) The mean does change. The mean is calculated by summing all the data values and dividing by the number of data values. If the highest value is increased by 10 and the lowest is decreased by 10, the sum of the data values changes, which in turn changes the mean.
(b) The median may or may not change. The median is the middle value when the data values are arranged in ascending order. If the data set is large and the changes to the highest and lowest values do not affect the middle value(s), then the median will not change. However, if the data set is small or the changes to the highest and lowest values do affect the middle value(s), then the median will change.
(c) It is possible for the mode to change, but it depends on the data set. The mode is the data value(s) that occurs most frequently. If the changes to the highest and lowest values create a new value that occurs more frequently than the previous mode, then the mode will change. However, if the changes do not affect the frequency of the data values, then the mode will not change.
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