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The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 82° is changed to 94°, which of the following measures changes the most and what is the new value?
IQR 34°
Range 48°
Mean 81.4°
Median 84°

User Nbsp
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1 Answer

1 vote

Answer:

(d) Median 84°

Explanation:

You want to know the effect on various statistics of changing the value 82 to 94 in the data ...

{57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105}

Measures of variation

Changing a middle value in the list will have no effect on either the range or the IQR.

Measures of center

Changing a value from 82 to 94 adds 12 to the total of the 12 data values. This will increase the mean by 12/12 = 1 degrees to about 81.4.

The median value is currently the average of 77 and 82. Replacing 82 with 94, changes the order so that the median will be the average of 77 and 91. That is the median will increase by 9/2 = 4.5 degrees.

The measure that changes the most is the median. Its new value is 84°, choice D.

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User Ed Gonzalez
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