Question

question #14 a data set consisting of 7 values has a median of 15 and a mean of 13. one of the data values is 20. suppose the value 20 in the data set is replaced with the value 22. which statement is true? a the mean increases, but the median stays the same. b the mean stays the same, but the median increases. c the mean increases, but the median decreases. d the mean decreases, but the median increases. question #15 the data below show the time that four friends spent studying each day for a week. the data for which student has the largest inter - quartile range? a john b vanessa c ashley d eric

Explanation:

Question #14

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here $n = 7$ and $\bar{x}=13$, so $\sum_{i=1}^{7}x_{i}=13\times7 = 91$.

Step2: Analyze change in sum

The original sum is 91. When 20 is replaced by 22, the new sum is $91-20 + 22=93$. The new mean is $\frac{93}{7}\approx13.29$, so the mean increases.

Step3: Recall median concept

For a data - set with $n = 7$ (odd number of values), the median is the 4th - ordered value. Since we are just changing one of the non - median values (20 to 22), the position of the median value in the ordered list does not change, so the median stays the same.

The inter - quartile range (IQR) is $Q_{3}-Q_{1}$. In a box - and - whisker plot, the length of the box represents the IQR.
By observing the box - and - whisker plots of John, Vanessa, Ashley, and Eric, we can see that Ashley's box has the largest length.

Answer:

A. The mean increases, but the median stays the same.

Question #15