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Chapter 3: Problem 125

The heights of five starting players on a basketball team have a mean of 76 inches, a median of 78 inches, and a range of 11 inches. a. If the tallest of these five players is replaced by a substitute who is 2 inches taller, find the new mean, median, and range. b. If the tallest player is replaced by a substitute who is 4 inches shorter, which of the new values (mean, median, range) could you determine, and what would their new values be?

Short Answer

Expert verified
a. The new mean will be 76.4 inches, the median will remain at 78 inches, and the range will increase to 13 inches. b. The new mean will be 75.2 inches and the median will remain at 78 inches. We cannot determine the new range.

Step by step solution

01

Understand the impact on the team if tallest player is replaced by a 2 inch taller substitute

Assuming that the tallest player is part of the 76 inches mean height. Replacing this player by a substitute 2 inches taller would add an extra 2 inches, which should be divided by the number of players, which is 5. So the new mean is 76 inches old mean + 2 inches/5 = 76.4 inches.
02

Determine the Validity of the old median

The median isn鈥檛 affected by extreme values, so it stays at 78 inches.
03

Compute the new range

The original range is 11 inches. With the substitute who is 2 inches taller, the range would increase by the same amount of 2 inches and would be 13 inches.
04

Understand the impact on the team if the tallest player is replaced by a 4 inch shorter substitute

Assuming that the tallest player is part of the 76 inches mean height. Replacing this player by a substitute 4 inches shorter would reduce 4 inches which should be divided by the number of players, which is 5. So the new mean is 76 inches old mean - 4 inches / 5 = 75.2 inches.
05

Determine the Validity of the old median

Again, the median isn鈥檛 affected by extreme values, so it stays at 78 inches.
06

Unable to compute the new range

While we know the tallest player is 4 inches shorter, we don鈥檛 know whether this is the shortest player originally or not. So, we can't find the new range.

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