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Select the outlier in the data set.\newline4,69,75,76,79,85,89,974, 69, 75, 76, 79, 85, 89, 97

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Q. Select the outlier in the data set.\newline4,69,75,76,79,85,89,974, 69, 75, 76, 79, 85, 89, 97
  1. List Data Set: List the data set and observe the values to identify any number that appears to be significantly different from the rest of the numbers.\newlineData set: 4,69,75,76,79,85,89,974, 69, 75, 76, 79, 85, 89, 97\newlineObservation: The number 44 seems to be much lower than all other numbers in the set.
  2. Calculate Mean: Calculate the mean (average) of the data set.\newlineMean = (4+69+75+76+79+85+89+97)/8(4 + 69 + 75 + 76 + 79 + 85 + 89 + 97) / 8\newlineMean = (574)/8(574) / 8\newlineMean = 71.7571.75
  3. Calculate Standard Deviation: Calculate the standard deviation of the data set. This involves several sub-steps, but for the purpose of identifying an outlier, a rough estimate or comparison of how far each number is from the mean may suffice.
  4. Compare to Mean: Compare each number in the set to the mean to see which one is farthest away.\newline- 44 is 67.7567.75 units away from the mean.\newline- 6969 is 2.752.75 units away from the mean.\newline- 7575 is 3.253.25 units away from the mean.\newline- 7676 is 4.254.25 units away from the mean.\newline- 7979 is 7.257.25 units away from the mean.\newline- 67.7567.7500 is 67.7567.7511 units away from the mean.\newline- 67.7567.7522 is 67.7567.7533 units away from the mean.\newline- 67.7567.7544 is 67.7567.7555 units away from the mean.\newlineClearly, 44 is significantly farther from the mean than all other numbers.
  5. Identify Outlier: Conclude which number is the outlier based on the comparison.\newlineThe number 44 is the outlier because it is significantly farther from the mean than any other number in the set.

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