Question

How will adding the value 75 affect the mean and median of the data set 1, 5, 7, 9 , 9, 10? * A.The median increases less than the mean increases. B. The mean and the median increase by the same amount. C.The mean increases and the median stays the same. D.The median increases and the mean stays the same.

Answer 1

{1,5,7,  9,9,10} is the original set. The median is the middle most value which is between 7 and 9 (those two values are tied for the middle most values). Add them up and divide by 2: 
(7+9)/2 = 16/2 = 8

The median of the original set is 8

The mean of the original set is approximately 6.83
Because we add up the values and divide by 6 (there are six data values)
1+5+7+9+9+10 = 41
41/6 = 6.83
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Now let's add 75 to the list of values. The list is now
{1, 5, 7, 9, 9, 10, 75}
The median becomes 9 which is shown in bold below
{1, 5, 7, 9, 9, 10, 75}
There are 3 values to the left of the median. There are 3 values to the right of the median.

The new mean is (1+5+7+9+9+10+75)/7 = 16.57 approximately

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Summary so far:
Old Median = 8
New Median = 9

Old Mean = 6.83
New Mean = 16.57

The medians are exact. The means are approximate to two decimal places.

So we can see that the mean increases dramatically compared to the median. This is why with large outliers, the median is always a better measure of center. The mean is always pulled toward the outlier. In the second data set, the distribution is skewed to the right (thanks to the outlier on the right pulling on the tail).

Answer: Choice A) The median increases less than the mean increases.