Question

determining the effect of outliers
fredrick hit 14, 18, 13, 12, 12, 16, 13, 12, 1, and 15 home runs in 10 seasons of play. which statements are correct?
check all that apply.
□ fredricks data set contains an outlier.
□ the median value is 12 home runs.
☑ the mean value is about 12.6 home runs.
□ the median describes fredricks data more accurately than the mean.
□ the mean value stays the same when the outlier is not included in the data set.

Explanation:

Step1: Identify outlier in data

Data set: $1, 12, 12, 12, 13, 13, 14, 15, 16, 18$
The value $1$ is far from other values, so it is an outlier.

Step2: Calculate median of data

For 10 values, median = $\frac{5^{th}+6^{th}}{2} = \frac{13+13}{2}=13$

Step3: Calculate mean of full data

Mean = $\frac{1+12+12+12+13+13+14+15+16+18}{10} = \frac{126}{10}=12.6$

Step4: Calculate mean without outlier

Mean (no outlier) = $\frac{12+12+12+13+13+14+15+16+18}{9} = \frac{125}{9}\approx13.89$

Step5: Compare median/mean accuracy

Since there is an outlier, median (unaffected by outlier) describes data better than mean.

Answer:

• Fredrick's data set contains an outlier.
• The mean value is about 12.6 home runs.
• The median describes Fredrick's data more accurately than the mean.