what is the standard deviation of these numbers 7 9 7 10 8 7 9
To calculate the standard deviation of a set of numbers, you need to follow these steps:
1. Find the mean (average) of the numbers. To do this, add up all the numbers and divide the sum by the total count of numbers.
(7 + 9 + 7 + 10 + 8 + 7 + 9) / 7 = 57 / 7 = 8.14 (rounded to two decimal places)
2. Subtract the mean from each number in the set. The resulting values are called deviations from the mean.
Deviations: (-1.14) 0 (-1.14) 1.86 (-0.14) (-1.14) 0.86
3. Square each deviation. This is done to get rid of negative values and emphasize differences from the mean.
Squared deviations: 1.3 0 1.3 3.46 0.02 1.3 0.74
4. Find the mean of the squared deviations. Sum up all the squared deviations and divide by the total count of numbers.
(1.3 + 0 + 1.3 + 3.46 + 0.02 + 1.3 + 0.74) / 7 = 8.12 / 7 = 1.16 (rounded to two decimal places)
5. Calculate the square root of the mean of the squared deviations. This is the standard deviation.
Square root of 1.16 = 1.08 (rounded to two decimal places)
Therefore, the standard deviation of the given set of numbers (7, 9, 7, 10, 8, 7, 9) is approximately 1.08.