To identify the outlier in the data set \( {7, 75, 79, 80, 83, 84, 90, 96, 98} \), we can look for a number that is significantly lower or higher than the others.
In this case, the number \(7\) stands out as it is much lower than the other values, which are all above \(75\). Therefore, \(7\) is the outlier.
Next, let's consider the effect of removing the outlier on the mean of the data set.
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Calculate the mean of the original data set:
- Sum of the numbers: \(7 + 75 + 79 + 80 + 83 + 84 + 90 + 96 + 98 = 602\)
- Number of data points: \(9\)
- Mean = \(\frac{602}{9} \approx 66.89\)
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Now, remove the outlier \(7\) and recalculate the mean for the remaining numbers \( {75, 79, 80, 83, 84, 90, 96, 98} \):
- Sum of the numbers: \(75 + 79 + 80 + 83 + 84 + 90 + 96 + 98 = 585\)
- Number of data points: \(8\)
- Mean = \(\frac{585}{8} = 73.125\)
Finally, compare the two means:
- Original mean with the outlier = \(66.89\)
- New mean without the outlier = \(73.125\)
Since the new mean \(73.125\) is greater than the original mean \(66.89\), we can conclude that removing the outlier \(7\) would increase the mean of the data set.