High School

This data is from a sample. Calculate the mean, standard deviation, and variance for the following numbers:

28.2, 38.4, 46.5, 15.9, 10.7, 34.4, 34, 17.4, 23.9

Please show the answers to 2 decimal places.

Answer :

Final answer:

The mean of the given data set is 27.71, the variance is 111.94, and the standard deviation is 10.59.

Explanation:

To calculate the mean, standard deviation, and variance of the given data set, follow these steps:

  1. Add up all the numbers: 28.2 + 38.4 + 46.5 + 15.9 + 10.7 + 34.4 + 34 + 17.4 + 23.9 = 249.4
  2. Count the total number of values in the data set: 9
  3. Calculate the mean by dividing the sum by the count: 249.4 / 9 = 27.71 (rounded to 2 decimal places)
  4. Subtract the mean from each value and square the result:
  5. (28.2 - 27.71)^2 = 0.19
  6. (38.4 - 27.71)^2 = 114.49
  7. (46.5 - 27.71)^2 = 351.56
  8. (15.9 - 27.71)^2 = 139.96
  9. (10.7 - 27.71)^2 = 292.46
  10. (34.4 - 27.71)^2 = 44.89
  11. (34 - 27.71)^2 = 39.69
  12. (17.4 - 27.71)^2 = 107.29
  13. (23.9 - 27.71)^2 = 14.49
  14. Calculate the variance by finding the average of the squared differences: (0.19 + 114.49 + 351.56 + 139.96 + 292.46 + 44.89 + 39.69 + 107.29 + 14.49) / 9 = 111.94 (rounded to 2 decimal places)
  15. Calculate the standard deviation by taking the square root of the variance: sqrt(111.94) = 10.59 (rounded to 2 decimal places)

Learn more about calculating mean, standard deviation, and variance here:

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