. Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. 15, 42, 53, 7, 9, 12, 14, 28, 47
1. find the mean
2. find the results of (mean - each data value)
3. square each of those results, then find their sum
4. divide that sum by 9
5. take the square root of that result
To find the standard deviation for the given data, follow these steps:
Step 1: Calculate the mean (average) of the data set.
- Add up all the numbers: 15 + 42 + 53 + 7 + 9 + 12 + 14 + 28 + 47 = 227
- Divide the sum by the number of data points: 227 / 9 = 25.2
Step 2: Calculate the deviations from the mean.
- Subtract the mean from each data point and write down the result:
15 - 25.2 = -10.2
42 - 25.2 = 16.8
53 - 25.2 = 27.8
7 - 25.2 = -18.2
9 - 25.2 = -16.2
12 - 25.2 = -13.2
14 - 25.2 = -11.2
28 - 25.2 = 2.8
47 - 25.2 = 21.8
Step 3: Square each deviation.
- Take each deviation from Step 2 and square it:
(-10.2)^2 = 104.04
(16.8)^2 = 282.24
(27.8)^2 = 772.84
(-18.2)^2 = 331.24
(-16.2)^2 = 262.44
(-13.2)^2 = 174.24
(-11.2)^2 = 125.44
(2.8)^2 = 7.84
(21.8)^2 = 475.24
Step 4: Calculate the variance.
- Add up all the squared deviations from Step 3:
104.04 + 282.24 + 772.84 + 331.24 + 262.44 + 174.24 + 125.44 + 7.84 + 475.24 = 2545.16
- Divide the sum by the number of data points (9) to get the variance: 2545.16 / 9 = 282.8
Step 5: Calculate the standard deviation.
- Take the square root of the variance from Step 4 to get the standard deviation:
√282.8 ≈ 16.8
Rounding your answer to one more decimal place than the original data, the standard deviation is approximately 16.8.