Select the outlier in the data set. 7, 68, 80, 83, 87, 89, 91, 96 If the outlier were removed from the data set, would the mean increase or decrease? Choices: (A)increase (B)decrease

Question

Select the outlier in the data set. 7, 68, 80, 83, 87, 89, 91, 96  If the outlier were removed from the data set, would the mean increase or decrease?   Choices: (A)increase (B)decrease

Bytelearn · Accepted Answer

Identify Outlier: Identify the outlier in the given data set: 7, 68, 80, 83, 87, 89, 91, 96. An outlier is a data point that is significantly different from the rest of the data. We can often spot an outlier by looking for a number that is much smaller or larger than the rest. In this case, 7 is much smaller than all other numbers in the set, so it is likely the outlier.Confirm Outlier: To confirm that 7 is an outlier, we can calculate the interquartile range (IQR) and then determine the lower and upper bounds for outliers. However, since 7 is significantly lower than the rest of the data and the next smallest number is 68, we can reasonably conclude that 7 is the outlier without further calculations.Calculate Mean with Outlier: Now, let's calculate the mean of the data set with and without the outlier to determine if the mean would increase or decrease upon its removal. First, calculate the mean with the outlier included: Mean = (7 + 68 + 80 + 83 + 87 + 89 + 91 + 96) / 8 Mean = (7 + 68 + 80 + 83 + 87 + 89 + 91 + 96) / 8 Mean = 601 / 8 Mean = 75.125Calculate Mean without Outlier: Next, calculate the mean without the outlier: Mean without outlier = (68 + 80 + 83 + 87 + 89 + 91 + 96) / 7 Mean without outlier = (68 + 80 + 83 + 87 + 89 + 91 + 96) / 7 Mean without outlier = 594 / 7 Mean without outlier = 84.857 approximatelyCompare Means: Compare the two means: Mean with outlier = 75.125 Mean without outlier = 84.857 Since the mean without the outlier is greater than the mean with the outlier, removing the outlier would increase the mean.Conclusion: The outlier in the data set is 7, and removing it would increase the mean. Therefore, the correct choice is (A) increase.

Select the outlier in the data set. $\newline$ $7, 68, 80, 83, 87, 89, 91, 96$ $\newline$ If the outlier were removed from the data set, would the mean increase or decrease? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease

Full solution

More problems from Identify an outlier and describe the effect of removing it

Related topics

Select the outlier in the data set.\newline7,68,80,83,87,89,91,967, 68, 80, 83, 87, 89, 91, 967,68,80,83,87,89,91,96\newlineIf the outlier were removed from the data set, would the mean increase or decrease?\newlineChoices:\newline(A)increase\newline(B)decrease

Select the outlier in the data set. $\newline$ $7, 68, 80, 83, 87, 89, 91, 96$ $\newline$ If the outlier were removed from the data set, would the mean increase or decrease? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease