Question

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 cm and 33 cm. Lara found out that they were misreading the longest length. It was actually 88 cm, not 33 cm. How will this length increasing affect the mean and median?

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.

Answer 1

Correcting the length of the longest fish from 33 cm to 88 cm will increase the mean but will not affect the median as the median is determined by the fourth fish in a dataset of 7, which remains unchanged.

Step-by-step explanation:

The question involves understanding how changing one data point in a set affects statistical measures such as the mean and median.

The mean, or average, is calculated by summing all the lengths of the fish and dividing by the total number of fish. When the longest fish's length is corrected from 33 cm to 88 cm, the sum increases significantly, which will result in a higher mean once it's recalculated with the new sum.

The median, the middle value in an ordered list of numbers, will not change when you only modify the largest value unless the dataset has an even number of observations and the change affects the two middlemost numbers. Lara observed 7 fish, so the median is the length of the fourth fish, which is unaffected by the change in the length of the largest fish. Consequently, there would be no change to the median in this dataset.

Therefore, the correct answer to Lara's question is option B: The mean will increase, and the median will stay the same.