How do you find the Standard Deviation of
2, 5, 47, 11, 13, 48, 39, 36
To find the standard deviation of a set of numbers, you need to follow these steps:
Step 1: Find the mean (average) of the data set.
To calculate the mean, add up all the numbers in the data set and then divide the sum by the total number of values. In this case, we add 2+5+47+11+13+48+39+36 = 201, and since there are 8 values, the mean is 201/8 = 25.125.
Step 2: Calculate the deviation of each data point from the mean.
To do this, subtract the mean from each individual data point. For example, the deviation for the first data point 2 is 2 - 25.125 = -23.125.
Step 3: Square each deviation obtained in Step 2.
Take each deviation value calculated in Step 2, and square it. For example, (-23.125)^2 = 537.140625.
Step 4: Find the mean of the squared deviations.
Calculate the mean of the squared deviations by summing up all the squared deviations and then dividing by the total number of values. For example, adding up all the squared deviations gives us 537.140625 + 400.015625 + 446.265625 + 174.890625 + 147.890625 + 396.015625 + 151.015625 + 130.015625 = 2383.2499999999995. Since there are 8 values, the mean of the squared deviations is 2383.2499999999995/8 = 297.90625.
Step 5: Take the square root of the mean of the squared deviations obtained in Step 4.
Finally, to calculate the standard deviation, take the square root of the mean of the squared deviations. In this case, the square root of 297.90625 is approximately 17.253.
Therefore, the standard deviation of the given set of numbers (2, 5, 47, 11, 13, 48, 39, 36) is approximately 17.253.