28.03.2023 - 14:29

Calculate the mean and standard deviation for the following set of data. 1, 3, 4, 5, 7, 6, 8, 9, 10, 12

Calculate the mean and standard deviation for the following set of data.

1, 3, 4, 5, 7, 6, 8, 9, 10, 12

Answers (1)
  • ALEXZLAT
    April 7, 2023 в 19:12

    To calculate the mean (average) of a set of data, you add up all the values in the set and divide by the total number of values.

    So, for the given set of data: 1+3+4+5+7+6+8+9+10+12 = 65 There are 10 values in the set.

    Therefore, the mean is: 65/10 = 6.5

    To calculate the standard deviation, you need to find the difference between each value in the set and the mean, square the differences, find the average of the squared differences, and then take the square root of that average.

    Here are the steps to calculate the standard deviation for the given set of data:

    1. Find the mean: 6.5

    2. Subtract the mean from each value in the set: (1-6.5), (3-6.5), (4-6.5), (5-6.5), (7-6.5), (6-6.5), (8-6.5), (9-6.5), (10-6.5), (12-6.5) -5.5, -3.5, -2.5, -1.5, 0.5, -0.5, 1.5, 2.5, 3.5, 5.5

    3. Square each of these differences: 30.25, 12.25, 6.25, 2.25, 0.25, 0.25, 2.25, 6.25, 12.25, 30.25

    4. Find the average of the squared differences: (30.25+12.25+6.25+2.25+0.25+0.25+2.25+6.25+12.25+30.25)/10 = 13.05

    5. Take the square root of the average: sqrt(13.05) ≈ 3.61

    Therefore, the standard deviation of the given set of data is \approx imately 3.61.

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