If the data set is {5, 7, 8, 9, 10}, what is the standard deviation?

If the data set is {5, 7, 8, 9, 10}, what is the standard deviation?

Step 1: Find the mean (average) of the data set. Add all the numbers together: 5 + 7 + 8 + 9 + 10 = 39. Then divide by the number of values (5): 39 / 5 = 7.8.
Step 2: Calculate the variance. For each number in the data set, subtract the mean (7.8) and square the result: (5 - 7.8)², (7 - 7.8)², (8 - 7.8)², (9 - 7.8)², (10 - 7.8)².
Step 3: Calculate each squared difference: (5 - 7.8)² = 7.84, (7 - 7.8)² = 0.64, (8 - 7.8)² = 0.04, (9 - 7.8)² = 1.44, (10 - 7.8)² = 4.84.
Step 4: Add all the squared differences together: 7.84 + 0.64 + 0.04 + 1.44 + 4.84 = 14.8.
Step 5: Divide the total squared differences by the number of values (5) to find the variance: 14.8 / 5 = 2.96.
Step 6: Find the standard deviation by taking the square root of the variance: √2.96 ≈ 1.72.

Mean – The average of a data set, calculated by summing all values and dividing by the number of values.
Variance – A measure of how much the values in a data set differ from the mean, calculated as the average of the squared differences from the mean.
Standard Deviation – The square root of the variance, representing the average distance of each data point from the mean.