Select the outlier in the data set. 4, 68, 76, 77, 83, 85, 87, 95, 98 If the outlier were removed from the data set, would the mean increase or decrease? Choices: (A)increase (B)decrease

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Select the outlier in the data set. 4, 68, 76, 77, 83, 85, 87, 95, 98  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 data set. To find the outlier, we can look for a number that is significantly different from the rest of the numbers in the set. In this case, the number 4 stands out as it is much lower than all other numbers.Determine Outlier Using IQR: Determine if 4 is an outlier using the interquartile range (IQR) method. First, we need to find the quartiles (Q1, Q2, and Q3) of the data set. Since the data set is already ordered, we can easily find the median (Q2), which is 83. The lower half of the data set is 4, 68, 76, 77, and the upper half is 85, 87, 95, 98. The median of the lower half is 72 (average of 68 and 76), which is Q1, and the median of the upper half is 91 (average of 87 and 95), which is Q3. Next, calculate the IQR: IQR = Q3 - Q1 = 91 - 72 = 19. Now, calculate the lower bound for outliers: Q1 - 1.5*IQR = 72 - 1.5*19 = 72 - 28.5 = 43.5. Since 4 is less than 43.5, it is considered an outlier.Calculate Mean with Outlier: Calculate the mean of the data set with and without the outlier. First, calculate the mean with the outlier: (4 + 68 + 76 + 77 + 83 + 85 + 87 + 95 + 98) / 9 = 673 / 9 ≈ 74.78. Next, calculate the mean without the outlier: (68 + 76 + 77 + 83 + 85 + 87 + 95 + 98) / 8 = 669 / 8 ≈ 83.63.Determine Mean Change: Determine if the mean would increase or decrease after removing the outlier. Comparing the two means calculated in Step 3, we see that the mean without the outlier (83.63) is higher than the mean with the outlier (74.78). Therefore, removing the outlier would increase the mean.

Select the outlier in the data set. $\newline$ $4, 68, 76, 77, 83, 85, 87, 95, 98$ $\newline$ If the outlier were removed from the data set, would the mean increase or decrease? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease

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Select the outlier in the data set.\newline4,68,76,77,83,85,87,95,984, 68, 76, 77, 83, 85, 87, 95, 984,68,76,77,83,85,87,95,98\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. $\newline$ $4, 68, 76, 77, 83, 85, 87, 95, 98$ $\newline$ If the outlier were removed from the data set, would the mean increase or decrease? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease