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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 58° is changed to 101°, which of the following measures changes the most and what is the new value?

Median 86.5°
Mean 84°
Range 48°
IQR 32°

User Wakurth
by
4.4k points

1 Answer

4 votes

Answer:

(a) Median, 86.5

Explanation:

You want to know which measure changes the most, and its new value, when 58 is changed to 101 in the given list.

Old values

The sorted list is ...

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

The median is the average of the 6th and 7th values: (77+82)/2 = 79.5.

The mean is the sum divided by 12, about 80.4.

The range is the difference of highest and lowest: 105-57 = 48.

The IQR is the difference between the average of the 9th and 10th numbers and the average of the 3rd and 4th numbers:

(95+100)/2 -(61+66)/2 = 34

New values

The sorted list after the change of values is ...

{57, 61, 66, 71, 77, 82, 91, 95, 100, 101, 102, 105}

The median is (82+91)/2 = 86.5, a change of 86.5 -79.5 = 7.

The mean is 84, a change of about 3.6.

The range is the same at 48, a change of 0.

The IQR is (100+101)/2 -(66 +71)/2 = 32, a change of -2.

The measure that changed the most is the median, which has a new value of 86.5, matching choice A.

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User Steffen Mangold
by
4.6k points