Question

in the data from the previous problem: 88, 90, 15, 75, 95, 82, 80
what affect does the book with only 15 pages have on the mean and the median.
○ it doesnt affect either the median or the mean much.
○ it pulls the value of the mean down and also pulls the median up.
○ it pulls the median and the mean both down.
○ it doesnt affect the median, but it pulls down the value of the mean.

Explanation:

Step1: Calculate mean with 15

Sum = 88+90+15+75+95+82+80 = 525; Mean = 525/7 = 75.

Step2: Calculate mean without 15

Sum = 525-15=510; Mean = 510/6=85. So 15 pulls mean down.

Step3: Find median with 15

Sorted data: 15,75,80,82,88,90,95. Median = 82.

Step4: Find median without 15

Sorted data:75,80,82,88,90,95. Median = (82+88)/2=85? No, wait—original has 7 data points (odd), median is 4th value=82. If 15 is removed, 6 data points (even), median is average of 3rd and 4th: (82+88)/2=85? No, correction: Wait, no—wait the question is "the effect of the book with 15 pages" (i.e., including it vs not including it). Wait no: actually, median is resistant to outliers. For the original data with 15, sorted is [15,75,80,82,88,90,95] (median=82). If we remove the outlier 15, sorted data is [75,80,82,88,90,95]—median is (82+88)/2=85? Wait no, no—the question is: when 15 is present (as an outlier), how does it affect mean vs median compared to if it wasn't there? The mean drops from 85 to 75 (pulled down). The median changes from 85 (without 15) to 82 (with 15)? Wait no, wait count: original data has 7 values (including 15): n=7, median is position (7+1)/2=4th value=82. Without 15: n=6, median is average of 3rd and 4th values: positions 3 and 4 are 82 and 88, so median=85. So including 15 makes median go from 85 to 82 (pulls down slightly?), but wait—wait no, the key point is: median is resistant to outliers. The outlier 15 is an extreme low value. The mean is affected by all values, so it's pulled down. The median is the middle value—adding 15 (a low outlier) shifts the sorted list to include it at the start, but the middle value (4th in 7 values) is still 82 (same as the 3rd value in the 6-value list without 15? Wait no, let's recheck: original data with 15: [15,75,80,82,88,90,95] → median=82. Data without 15: [75,80,82,88,90,95] → median=(82+88)/2=85. So including 15 lowers the median by 3, but compared to the mean's drop from 85 to 75 (10 points), the median change is small. But wait the options: the last option says "It doesn't affect the median, but it pulls down the value of the mean." Is that correct? Because the median change is minimal (or maybe in the context of the question, the outlier doesn't significantly affect the median). The mean is pulled down a lot, median is almost unchanged. So the correct option is the last one.

Answer:

D. It doesn't affect the median, but it pulls down the value of the mean.