Select the outlier in the data set. 6, 47, 51, 52, 54, 56, 57, 59, 69 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. 6, 47, 51, 52, 54, 56, 57, 59, 69  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. The data set is: 6, 47, 51, 52, 54, 56, 57, 59, 69. An outlier is a data point that is significantly different from the other data points. We can use the interquartile range (IQR) method to identify outliers.Calculate Quartiles: Calculate the quartiles (Q1, Q2, Q3) of the data set. To find the quartiles, we need to arrange the data in ascending order and then find the median (Q2), the median of the lower half (Q1), and the median of the upper half (Q3). The data set in ascending order is already given: 6, 47, 51, 52, 54, 56, 57, 59, 69. The median (Q2) is the middle number, which is 54. The lower half of the data set is 6, 47, 51, 52, and its median (Q1) is 47. The upper half of the data set is 56, 57, 59, 69, and its median (Q3) is 57.Calculate IQR: Calculate the interquartile range (IQR). IQR = Q3 - Q1 IQR = 57 - 47 IQR = 10Determine Bounds: Determine the bounds for potential outliers. The lower bound is Q1 - 1.5 * IQR, and the upper bound is Q3 + 1.5 * IQR. Lower bound = 47 - 1.5 * 10 = 47 - 15 = 32 Upper bound = 57 + 1.5 * 10 = 57 + 15 = 72 Any data point below 32 or above 72 is considered an outlier.Identify Outlier(s): Identify the outlier(s) based on the bounds. Looking at the data set, the number 6 is below the lower bound of 32, so it is an outlier. There are no data points above the upper bound of 72.Calculate Mean with Outlier: Calculate the mean of the data set with and without the outlier to determine the effect on the mean. First, calculate the mean with the outlier: Mean with outlier = (6 + 47 + 51 + 52 + 54 + 56 + 57 + 59 + 69) / 9 Mean with outlier = 451 / 9 Mean with outlier = 50.11 (rounded to two decimal places)Calculate Mean without Outlier: Now, calculate the mean without the outlier: Mean without outlier = (47 + 51 + 52 + 54 + 56 + 57 + 59 + 69) / 8 Mean without outlier = 445 / 8 Mean without outlier = 55.625Compare Means: Compare the means to determine if the mean would increase or decrease upon the removal of the outlier. The mean with the outlier is 50.11, and the mean without the outlier is 55.625. Since the mean without the outlier is greater than the mean with the outlier, the mean would increase if the outlier were removed.

Select the outlier in the data set. $\newline$ $6, 47, 51, 52, 54, 56, 57, 59, 69$ $\newline$ 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.\newline6,47,51,52,54,56,57,59,696, 47, 51, 52, 54, 56, 57, 59, 696,47,51,52,54,56,57,59,69\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. $\newline$ $6, 47, 51, 52, 54, 56, 57, 59, 69$ $\newline$ If the outlier were removed from the data set, would the mean increase or decrease? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease