ACT Preparation / Unit 15 ACT 1415 worked example, 60 to 90 seconds
What a New Value Does
The idea
To predict how one added value changes a data set, work in three steps. First, compare the value with the current mean: a value above the mean raises it, a value below lowers it, and an equal value leaves it unchanged. Second, consider the median: one added value shifts it by at most half a position, so it changes little. Third, check the extremes: a new maximum or minimum changes the range, while the IQR changes little.
In practice
Worked example: the data 4, 6, 7, 9, 14 have mean 8, median 7 and range 10. Adding 30: the mean becomes 70/6, about 11.7; the median becomes the average of 7 and 9, which is 8; and the range becomes 26. The mean jumped by more than three, while the median moved by one.
Where people slip
A value equal to the mean leaves the mean unchanged, but it still changes the count, and it can shift the median.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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