Calculate Standard Deviation

Sample Scores on a Test Out of 40:

24, 37, 28, 27, 28, 29, 25, 28,
24, 25, 26, 34, 38, 28, 40, 31, 20,
24, 25, 25, 25, 29, 38, 35, 30

  1. Calculate mean: 755 /26 = 29.0

  2. Find out how far away from the mean each number is:

    24 - 29 = -5
    37 - 29 = +8
    28 -29 = -1
    27 -29 = -2
    28 - 29 = -1
    29 - 29 = 0
    25 - 29 = -4
    28 - 29 = -1
    24 - 29 = -5
    25 - 29 = -4
    26 - 29 = -3

    etc.

    Try to caluculate the average difference.

  3. Want to find the average distance from the mean, but one cannot take the mean of this column, because the sum of the distances from the mean will always total 0.

  4. So need to get rid of the + and - signs.

      . . . so square the items in column:

    24 -29 = -5 = 25
    37 -29 = +8 = 64
    28 -29 = -1 = 1
    27 -29 = -2 = 4
    28 - 29 = -1 = 1
    29 - 29 = 0 = 0
    25 - 29 = - 4 = 16

    etc. ________
    Total

  5. Take the average (mean) of the squares instead:

      add up the squares and divide by
      number of numbers in the column

    This is called the VARIANCE

  6. Take the square root ( to get back to where you were). The Standard Deviation is the square root of the Variance.

Measures of Variability.