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Lara is a wildlife researcher. They were analyzing the mean and median lengths of 7 fish their team had observed. The fish all had different lengths between
15cm and
33cm.
Lara found out that they were misreading the longest length. It was actually
88cm, not
33cm.
How will this length increasing affect the mean and median?
Choose 1 answer:
A Both the mean and median will increase.
B The mean will increase, and the median will stay the same.
(c) The mean will increase, and the median will decrease.
(D) The mean will stay the same, and the median will increase.

Lara is a wildlife researcher. They were analyzing the mean and median lengths of $7$ fish their team had observed. The fish all had different lengths between $15 \mathrm{~cm}$ and $33 \mathrm{~cm}$ . $\newline$ Lara found out that they were misreading the longest length. It was actually $88 \mathrm{~cm}$ , not $33 \mathrm{~cm}$ . $\newline$ How will this length increasing affect the mean and median? $\newline$ Choose $1$ answer: $\newline$ (A) Both the mean and median will increase. $\newline$ (B) The mean will increase, and the median will stay the same. $\newline$ (C) The mean will increase, and the median will decrease. $\newline$ (D) The mean will stay the same, and the median will increase.

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Quantities that combine to zero: word problems

Full solution

Q. Lara is a wildlife researcher. They were analyzing the mean and median lengths of

7

fish their team had observed. The fish all had different lengths between

15 \mathrm{~cm}

and

33 \mathrm{~cm}

.

\newline

Lara found out that they were misreading the longest length. It was actually

88 \mathrm{~cm}

, not

33 \mathrm{~cm}

.

\newline

How will this length increasing affect the mean and median?

\newline

Choose

1

answer:

\newline

(A) Both the mean and median will increase.

\newline

(B) The mean will increase, and the median will stay the same.

\newline

(C) The mean will increase, and the median will decrease.

\newline

(D) The mean will stay the same, and the median will increase.

Understand Data Set: To understand how the mean and median will be affected, we need to consider the original data set of fish lengths. Since we don't have the exact lengths of all $7$ fish, we can't calculate the exact mean and median. However, we can understand the impact on the mean and median conceptually.
Calculate Mean Impact: The mean (average) is calculated by adding all the lengths of the fish and dividing by the number of fish. Increasing the length of the longest fish from $33\,\text{cm}$ to $88\,\text{cm}$ will add more to the total sum of lengths. Since the number of fish remains the same, the mean will increase.
Calculate Median Impact: The median is the middle value when the lengths are ordered from smallest to largest. With $7$ fish, the median is the $4$ th value. Unless the $4$ th value (which is the median) changes, the median will remain the same. Since we are only changing the longest length (the $7$ th value), the median will stay the same.
Final Comparison: Therefore, the mean will increase because the total sum of lengths increases, but the median will not change because the middle value remains the same.

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