question 6 (2 points)\nwhat effect does eliminating the highest value, 180, from the data set have on the…
question 6 (2 points)\nwhat effect does eliminating the highest value, 180, from the data set have on the mean and median?\n25, 50, 50, 60, 70, 85, 85, 90, 90, 180\nthe mean decreases (increases, decreases) from ______ to 67.22 (round to the nearest hundredth)\nthe median decreases (increases, decreases) from 77.5 to 70\nblank 1: decreases\nblank 2:\nblank 3: 67.22\nblank 4: decreases\nblank 5: 77.5\nblank 6: 70
Answer
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