Question

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.

Explanation:

Step1: Calculate the mean

Sum the data: \(13 + 11 + 16 + 12 + 42 + 8 = 102\). Divide by the number of data points (\(n = 6\)): \(\frac{102}{6} = 17\). So the mean is 17.

Step2: Find the median

Sort the data: \(8, 11, 12, 13, 16, 42\). Since \(n\) is even, median is the average of the middle two values: \(\frac{12 + 13}{2} = 12.5\). Wait, no—wait, middle two are 12 and 13? Wait, sorted list: 8, 11, 12, 13, 16, 42. The third and fourth values are 12 and 13. So median is \(\frac{12 + 13}{2} = 12.5\)? Wait, no, wait: 8, 11, 12, 13, 16, 42. The two middle numbers are 12 (third) and 13 (fourth). So median is \(\frac{12 + 13}{2} = 12.5\)? Wait, but let's check again. Wait, 6 data points: positions 1 - 6. Middle positions are 3 and 4. So values at 3: 12, 4: 13. So median is \(\frac{12 + 13}{2} = 12.5\). Wait, but wait, the options: one says median is 12.5, another 14.5. So median is 12.5. Then, the outlier here is 42, which is much larger. Mean is affected by outliers because it uses all values, median is not (since it's about the middle). So mean is more affected by outlier. Then, mean is 17 (from step1), so the first statement (mean is 17) is true. Median is 12.5 (step2), so that statement is true. Mean is more affected by outlier (since outlier 42 increases the mean), median is not. So the true statements: mean is 17, median is 12.5, mean is more affected by outlier. Wait, let's recheck mean: 13+11=24, +16=40, +12=52, +42=94, +8=102. 102/6=17. Correct. Median: sorted data 8,11,12,13,16,42. Middle two: 12 and 13. Average: (12+13)/2=12.5. Correct. So the true options: "The mean of this data set is 17", "The median is 12.5", "The mean is more affected by the outlier".

Answer:

The mean of this data set is 17, The median is 12.5, The mean is more affected by the outlier (corresponding to the checkboxes: the first, second, and fourth options).