Question

8 from unit 3, lesson 9
here is a data set.
-6 3 3 3 3 5 6 6 8 10
what effect does eliminating the lowest value, -6, from the data set have on the mean and median?

Explanation:

Step1: List original data

Original data: -6, 3, 3, 3, 3, 5, 6, 6, 8, 10 (n=10)

Step2: Calculate original mean

Mean = $\frac{-6+3+3+3+3+5+6+6+8+10}{10} = \frac{41}{10} = 4.1$

Step3: Find original median

Sorted data: -6,3,3,3,3,5,6,6,8,10. Median = $\frac{3+5}{2}=4$

Step4: Data without -6

New data: 3,3,3,3,5,6,6,8,10 (n=9)

Step5: Calculate new mean

Mean = $\frac{3+3+3+3+5+6+6+8+10}{9} = \frac{47}{9} \approx 5.22$

Step6: Find new median

Sorted new data: 3,3,3,3,5,6,6,8,10. Median = 5

Step7: Compare changes

Mean increases (4.1→~5.22); median increases (4→5)

Answer:

Eliminating -6 increases both the mean and the median.