Question

Find the standard deviation. Round to the nearest hundredth. 23,18,28,36,15

Answer 1

To compute standard deviation for the data set 23, 18, 28, 36, 15, first calculate the mean, find the deviations, square them, calculate their mean and take the square root. The standard deviation is approximately 7.46.

Step-by-step explanation:

To find the standard deviation of the numbers 23, 18, 28, 36, 15, we first need to calculate the mean, which is the average of these numbers.

1. Add all the numbers: 23 + 18 + 28 + 36 + 15 = 120.
2. Divide by the number of values: 120 / 5 = 24. This is the mean.
3. Subtract the mean from each number to find the deviation of each number from the mean: (23-24), (18-24), (28-24), (36-24), (15-24). This results in -1, -6, 4, 12, -9 respectively.
4. Square each deviation: 1, 36, 16, 144, 81.
5. Find the mean of these squared deviations. Add them together and divide by the number of values: (1 + 36 + 16 + 144 + 81) / 5 = 55.6
6. Take the square root of this last mean to get the standard deviation: √55.6 ≈ 7.46.

Therefore, the standard deviation, rounded to the nearest hundredth, is 7.46.