Sample Standard Deviation Example Problem

This is a simple example of how to calculate sample variance and sample standard deviation. First, lets review the steps for calculating the sample standard deviation: Calculate the mean (simple average of the numbers).For each number: subtract the mean. Square the result.Add up all of the squared results.Divide this sum by one less than the number of data points (N - 1). This gives you the sample variance.Take the square root of this value to obtain the sample standard deviation. Example Problem You grow 20 crystals from a solution and measure the length of each crystal in millimeters. Here is your data: 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4 Calculate the sample standard deviation of the length of the crystals. Calculate the mean of the data. Add up all the numbers and divide by the total number of data points.(925412781193741254109694) / 20 140/20 7Subtract the mean from each data point (or the other way around, if you prefer... you will be squaring this number, so it does not matter if it is positive or negative).(9 - 7)2 (2)2 4(2 - 7)2 (-5)2 25(5 - 7)2 (-2)2 4(4 - 7)2 (-3)2 9(12 - 7)2 (5)2 25(7 - 7)2 (0)2 0(8 - 7)2 (1)2 1(11 - 7)2 (4)22 16(9 - 7)2 (2)2 4(3 - 7)2 (-4)22 16(7 - 7)2 (0)2 0(4 - 7)2 (-3)2 9(12 - 7)2 (5)2 25(5 - 7)2 (-2)2 4(4 - 7)2 (-3)2 9(10 - 7)2 (3)2 9(9 - 7)2 (2)2 4(6 - 7)2 (-1)2 1(9 - 7)2 (2)2 4(4 - 7)2 (-3)22 9Calculate the mean of the squared differences.(4254925011641609254994149) / 19 178/19 9.368This value is the sample variance. The sample variance is 9.368The population standard deviation is the square root of the variance. Use a calculator to obtain this number.(9.368)1/2 3.061The population standard deviation is 3.061 Compare this with the variance and population standard deviation for the same data.