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 ________ (increases, decreases) from ______ to ________ (round to the nearest hundredth).
the median ________ (increases, decreases) from ______ to ________.
blank 1:
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blank 6:

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 $\bar{x}_1=\frac{785}{10}=78.50$.

Step2: Calculate new mean

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

Step3: Calculate original median

For a data - set with $n = 10$ (an 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

For a data - set with $n = 9$ (an odd number of data points), the median is the $(\frac{n + 1}{2})$th ordered data point. The ordered data set without 180 is $25,50,50,60,70,85,85,90,90$. The 5th value is 70. So the new median $M_2 = 70$. The median decreases.

Answer:

Blank 1: decreases
Blank 2: 78.50
Blank 3: 67.22
Blank 4: decreases
Blank 5: 77.5
Blank 6: 70