Question

Kimberly collects data on the average temperatures in January in her state over the last 30 years. She then calculates the mean and median for the data set.
Kimberly decides to collect data from two more years and add them to her original data set. The first year, the average temperature is colder than it had been for any of her previous recorded data. The second year, the average temperature is warmer than for any of her previous data.


Which statement describes how adding the two new temperatures to Kimberly's data set could change the statistical measures?


A

The mean and median may both change.

B

The mean and median will both stay the same.

C

The median may change, but the mean will not change.

D

The mean may change, but the median will not change.

Answer 1

Answer:

D.) The mean may change, but the median will not change.

Step-by-step explanation:

By adding two new values to the existing dataset ; this two values are extreme values as described in the dataset.;

As the warmer will be the new minimum and the colder the new maximum .

The median value being the midpoint of the dataset when arranged in order will definitely not be affected by these new additions are at the beginning and end of the data set. Hence, the previous median points will Also be the new median points.

As for the mean, it has to do with calculation the average value, despite the number being at the extreme, the new points may take up any value and hence will affect the new sum and ultimately the obtained average.

Therefore,The mean may change, but the median will not change.