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: Order the data set

12, 12, 12, 13, 13, 14, 15, 16, 18, 19

Step2: Check for outliers

IQR = Q3 - Q1 = 16 - 12 = 4; Lower bound: $12 - 1.5\times4=6$, Upper bound: $16 + 1.5\times4=22$. All values are within bounds, no outliers.

Step3: Calculate the median

Even number of values: $\frac{13+14}{2}=13.5$

Step4: Calculate the mean

$\frac{12+12+12+13+13+14+15+16+18+19}{10}=\frac{126}{10}=12.6$

Step5: Compare median vs mean

Since there are no outliers, both describe the data, but the mean is 12.6, median 13.5. Without outliers (none exist), mean stays same.

Answer:

• The mean value is about 12.6 home runs.