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Select the outlier in the data set.\newline1,72,74,78,83,85,91,931, 72, 74, 78, 83, 85, 91, 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.\newline1,72,74,78,83,85,91,931, 72, 74, 78, 83, 85, 91, 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: 1,72,74,78,83,85,91,931, 72, 74, 78, 83, 85, 91, 93. An outlier is a data point that is significantly different from the other data points in a set. We can often spot an outlier by looking for a number that is much smaller or larger than the rest.
  2. Spot Outlier: Looking at the data set, 11 is much smaller than all other numbers, which are all above 7070. Therefore, 11 is the outlier.
  3. 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.\newlineFirst, calculate the mean with the outlier included:\newlineMean = (1+72+74+78+83+85+91+93)/8(1 + 72 + 74 + 78 + 83 + 85 + 91 + 93) / 8\newlineMean = 577/8577 / 8\newlineMean ≈72.125\approx 72.125
  4. Calculate Mean without Outlier: Next, calculate the mean without the outlier:\newlineMean = (72+74+78+83+85+91+93)/7(72 + 74 + 78 + 83 + 85 + 91 + 93) / 7\newlineMean = 576/7576 / 7\newlineMean ≈82.2857\approx 82.2857
  5. Compare Means: Comparing the two means, we see that the mean without the outlier (approximately 82.2982.29) is greater than the mean with the outlier (approximately 72.1372.13). Therefore, if the outlier were removed from the data set, the mean would increase.

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