To determine whether the mean or median better describes the shape of the data set (80, 95, 157, 95, 80, 75, 95, 75), we first need to calculate both the mean and the median.
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Mean:
- Add all the values: \(80 + 95 + 157 + 95 + 80 + 75 + 95 + 75 = 862\)
- Count the number of values: There are 8 values.
- Calculate the mean: \(\frac{862}{8} = 107.75\)
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Median:
- First, we need to arrange the data in ascending order: \(75, 75, 80, 80, 95, 95, 95, 157\).
- Since there are 8 values (an even number), the median will be the average of the 4th and 5th values.
- The 4th value is 80, and the 5th value is 95.
- Calculate the median: \(\frac{80 + 95}{2} = \frac{175}{2} = 87.5\).
Now we can summarize:
- The mean is 107.75.
- The median is 87.5.
Considering the skewness of the data (due to the high value of 157), the mean is likely affected more by this outlier than the median. Therefore, the median generally provides a better measure of central tendency in this case.
Thus, the correct response would be:
The median of 87.5 is the best measure of center to describe the shape of the data set.