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Diego is a wildlife researcher. They were analyzing the mean and median lengths of 9 whales their team had observed. The whales all had different lengths between 23m and 27m. Diego found out that they were misreading the shortest length. It was actually 20m, not 23m. How will this length decreasing affect the mean and median? Choose 1 answer: A Both the mean and median will decrease. (B) The mean will decrease, and the median will increase. (c) The mean will decrease, and the median will stay the same. (D) The mean will stay the same, and the median will decrease.

Diego is a wildlife researcher. They were analyzing the mean and median lengths of 99 whales their team had observed. The whales all had different lengths between 23 m 23 \mathrm{~m} and 27 m 27 \mathrm{~m} .\newlineDiego found out that they were misreading the shortest length. It was actually 20 m 20 \mathrm{~m} , not 23 m 23 \mathrm{~m} .\newlineHow will this length decreasing affect the mean and median?\newlineChoose 11 answer:\newline(A) Both the mean and median will decrease.\newline(B) The mean will decrease, and the median will increase.\newline(C) The mean will decrease, and the median will stay the same.\newline(D) The mean will stay the same, and the median will decrease.

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Q. Diego is a wildlife researcher. They were analyzing the mean and median lengths of 99 whales their team had observed. The whales all had different lengths between 23 m 23 \mathrm{~m} and 27 m 27 \mathrm{~m} .\newlineDiego found out that they were misreading the shortest length. It was actually 20 m 20 \mathrm{~m} , not 23 m 23 \mathrm{~m} .\newlineHow will this length decreasing affect the mean and median?\newlineChoose 11 answer:\newline(A) Both the mean and median will decrease.\newline(B) The mean will decrease, and the median will increase.\newline(C) The mean will decrease, and the median will stay the same.\newline(D) The mean will stay the same, and the median will decrease.
  1. Understand the mean effect: Understand the effect on the mean.\newlineThe mean (average) length of the whales is calculated by summing all the lengths and dividing by the number of whales. If the shortest length is decreased from 23 m23\,\text{m} to 20 m20\,\text{m}, the total sum of the lengths will decrease. Since the number of whales remains the same, the mean will decrease.
  2. Calculate mean change: Calculate the change in the mean.\newlineAssuming the other 88 whales' lengths remain unchanged, the decrease in total length is 3 m3\,\text{m} (from 23 m23\,\text{m} to 20 m20\,\text{m}). To find the change in the mean, we divide this decrease by the number of whales, which is 99.\newlineChange in mean = 3 m9=0.333 m\frac{3\,\text{m}}{9} = 0.333\,\text{m}\newlineThe mean will decrease by 0.333 m0.333\,\text{m}.
  3. Understand the median effect: Understand the effect on the median.\newlineThe median is the middle value when all lengths are ordered from smallest to largest. Since there are 99 whales, the median is the 55th whale's length. If the shortest whale's length changes from 23 m23\,\text{m} to 20 m20\,\text{m}, but all other lengths are between 23 m23\,\text{m} and 27 m27\,\text{m}, the median will remain the same because the 55th whale's length is unaffected by the change at the lower end of the dataset.

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