using the set of data below, which statements are true? check all that apply. 13, 11, 16, 12, 42, 8 the mean…

using the set of data below, which statements are true? check all that apply. 13, 11, 16, 12, 42, 8 the mean of this data set is 17. the median is 12.5. the median is 14.5. the mean is more affected by the outlier. the median is more affected by the outlier. the mean of this data set is 12.

using the set of data below, which statements are true? check all that apply. 13, 11, 16, 12, 42, 8 the mean of this data set is 17. the median is 12.5. the median is 14.5. the mean is more affected by the outlier. the median is more affected by the outlier. the mean of this data set is 12.

Answer

Answer:

  • The mean of this data set is 17.
  • The median is 12.5.
  • The mean is more affected by the outlier.

Explanation:

Step1: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $n = 6$, and $\sum_{i=1}^{6}x_{i}=13 + 11+16 + 12+42+8=102$. So $\bar{x}=\frac{102}{6}=17$.

Step2: Calculate the median

First, order the data set: $8,11,12,13,16,42$. Since $n = 6$ (an even - numbered data set), the median $M=\frac{12 + 13}{2}=12.5$.

Step3: Analyze the effect of the outlier

The outlier is 42. If we remove 42, the new data set is $8,11,12,13,16$. The new mean is $\frac{8 + 11+12+13+16}{5}=\frac{60}{5}=12$, a change of $17-12 = 5$. The new median is 12, a change of $12.5 - 12=0.5$. So the mean is more affected by the outlier.