Question

question 6 (2 points)
what effect does eliminating the highest value, 180, from the data set have on the mean and median?
25, 50, 50, 60, 70, 85, 85, 90, 90, 180
the mean decreases (increases, decreases) from ______ to 67.22 (round to the nearest hundredth)
the median decreases (increases, decreases) from 77.5 to 70
blank 1: decreases
blank 2:
blank 3: 67.22
blank 4: decreases
blank 5: 77.5
blank 6: 70

Explanation:

Step1: Calculate original mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 10$, and $\sum_{i=1}^{10}x_{i}=25 + 50+50 + 60+70+85+85+90+90+180=785$. So the original mean $\bar{x}_1=\frac{785}{10}=78.5$.

Step2: Calculate new mean

After eliminating 180, $n = 9$, and $\sum_{i = 1}^{9}x_{i}=785 - 180=605$. The new mean $\bar{x}_2=\frac{605}{9}\approx67.22$.

Step3: Calculate original median

For a data - set with $n = 10$ (even number of data points), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data points. The ordered data set is 25, 50, 50, 60, 70, 85, 85, 90, 90, 180. The 5th and 6th values are 70 and 85. So the original median $M_1=\frac{70 + 85}{2}=77.5$.

Step4: Calculate new median

After eliminating 180, $n = 9$ (odd number of data points). The median is the $(\frac{n + 1}{2})$th ordered data point. The ordered data set is 25, 50, 50, 60, 70, 85, 85, 90, 90. The 5th value is 70, so the new median $M_2 = 70$.

Answer:

Blank 1: decreases
Blank 2: 78.5
Blank 3: 67.22
Blank 4: decreases
Blank 5: 77.5
Blank 6: 70