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Select the outlier in the data set.\newline8,62,66,73,77,80,84,938, 62, 66, 73, 77, 80, 84, 93\newlineIf the outlier were removed from the data set, would the mean increase or decrease?\newlineChoices:\newline(A)increase\newline(B)decrease

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Q. Select the outlier in the data set.\newline8,62,66,73,77,80,84,938, 62, 66, 73, 77, 80, 84, 93\newlineIf the outlier were removed from the data set, would the mean increase or decrease?\newlineChoices:\newline(A)increase\newline(B)decrease
  1. Identify Outlier: Identify the outlier in the given data set: 8,62,66,73,77,80,84,938, 62, 66, 73, 77, 80, 84, 93. To find the outlier, we can use the interquartile range (IQR) method. First, we need to calculate the first quartile (Q1Q1), the third quartile (Q3Q3), and then find the IQR (Q3−Q1Q3 - Q1). Any number that is more than 1.51.5 times the IQR below Q1Q1 or above Q3Q3 is considered an outlier.
  2. Calculate Quartiles: Since the data set is already in ascending order, we can find Q1Q_1 and Q3Q_3 by dividing the data set into four equal parts. For this data set, Q1Q_1 is the median of the first half, and Q3Q_3 is the median of the second half.\newlineThe first half of the data set: 88, 6262, 6666, 7373\newlineThe second half of the data set: 7777, 8080, Q3Q_300, Q3Q_311\newlineQ1Q_1 is the average of 6262 and 6666, and Q3Q_3 is the average of 8080 and Q3Q_300.\newlineQ3Q_388\newlineQ3Q_399
  3. Calculate IQR: Calculate the IQR: IQR=Q3−Q1=82−64=18\text{IQR} = Q3 - Q1 = 82 - 64 = 18.
  4. Determine Outlier Threshold: Determine the outlier threshold: Any number less than Q1−1.5×IQRQ1 - 1.5 \times IQR or greater than Q3+1.5×IQRQ3 + 1.5 \times IQR is an outlier.\newlineLower bound = Q1−1.5×IQR=64−1.5×18=64−27=37Q1 - 1.5 \times IQR = 64 - 1.5 \times 18 = 64 - 27 = 37\newlineUpper bound = Q3+1.5×IQR=82+1.5×18=82+27=109Q3 + 1.5 \times IQR = 82 + 1.5 \times 18 = 82 + 27 = 109
  5. Identify Outlier: Identify the outlier: The number 88 is below the lower bound of 3737, so it is an outlier.
  6. Calculate Mean: Calculate the mean of the original data set: (8+62+66+73+77+80+84+93)/8=543/8=67.875(8 + 62 + 66 + 73 + 77 + 80 + 84 + 93) / 8 = 543 / 8 = 67.875.
  7. Remove Outlier: Remove the outlier (8)(8) and calculate the new mean: (62+66+73+77+80+84+93)/7=535/7=76.4286(62 + 66 + 73 + 77 + 80 + 84 + 93) / 7 = 535 / 7 = 76.4286.
  8. Compare Mean: Compare the original mean 67.87567.875 with the new mean 76.428676.4286 after removing the outlier. The new mean is higher than the original mean.

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