Select the outlier in the data set. $\newline$ $2, 72, 80, 85, 87, 91, 95, 97, 99$ $\newline$ If the outlier were removed from the data set, would the mean increase or decrease? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease

View step-by-step help

Home

Math Problems

Algebra 1

Identify an outlier and describe the effect of removing it

Full solution

Q. Select the outlier in the data set.

\newline

2, 72, 80, 85, 87, 91, 95, 97, 99

\newline

If the outlier were removed from the data set, would the mean increase or decrease?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

Identify Outlier: Identify the outlier in the data set. $\newline$ To find the outlier, we can look for a number that is significantly different from the rest of the numbers in the set. In this case, the number $2$ stands out as being much lower than all other numbers, which are all $72$ or higher.
Confirm Outlier: Confirm that $2$ is an outlier by comparing it to the rest of the data. $\newline$ An outlier is typically a value that is much higher or lower than the other values in a data set. In this case, $2$ is much lower than the next lowest number, $72$ , which suggests that it is indeed an outlier.
Calculate Mean with Outlier: Calculate the mean of the original data set including the outlier. $\newline$ To calculate the mean, add all the numbers together and then divide by the number of values. $\newline$ Mean = $(2 + 72 + 80 + 85 + 87 + 91 + 95 + 97 + 99) / 9$ $\newline$ Mean = $(708) / 9$ $\newline$ Mean = $78.67$ (rounded to two decimal places)
Calculate Mean without Outlier: Calculate the mean of the data set without the outlier. $\newline$ Remove the outlier $2$ and then calculate the new mean. $\newline$ New Mean = $(72 + 80 + 85 + 87 + 91 + 95 + 97 + 99) / 8$ $\newline$ New Mean = $(706) / 8$ $\newline$ New Mean = $88.25$ (rounded to two decimal places)
Compare Means: Compare the two means to determine if the mean would increase or decrease without the outlier. The original mean was $78.67$ , and the new mean without the outlier is $88.25$ . Since $88.25$ is greater than $78.67$ , removing the outlier increases the mean.