What is the standard deviation of the data set?
Round the answer to the nearest tenth.
5, 9, 11, 4, 8, 9, 12
Here is a cute little video from the KhanAcademy
to show the basic method.
It will depend on how you were taught whether you divide by 7 or by 6.
You will have to check your notes or your textbook
https://www.khanacademy.org/math/statistics-probability/displaying-describing-data/sample-standard-deviation/v/sample-standard-deviation-and-bias
To calculate the standard deviation of a data set, follow these steps:
1. Find the mean (average) of the data set.
- Add up all the numbers in the data set: 5 + 9 + 11 + 4 + 8 + 9 + 12 = 58.
- Divide the sum by the number of data points: 58 / 7 = 8.3.
- The mean of the data set is 8.3.
2. Calculate the deviation of each data point from the mean.
- Subtract the mean from each data point:
- 5 - 8.3 = -3.3
- 9 - 8.3 = 0.7
- 11 - 8.3 = 2.7
- 4 - 8.3 = -4.3
- 8 - 8.3 = -0.3
- 9 - 8.3 = 0.7
- 12 - 8.3 = 3.7
3. Square each deviation.
- Square each calculated deviation:
- (-3.3)² = 10.9
- 0.7² = 0.49
- 2.7² = 7.29
- (-4.3)² = 18.49
- (-0.3)² = 0.09
- 0.7² = 0.49
- 3.7² = 13.69
4. Find the mean of the squared deviations.
- Add up all the squared deviations: 10.9 + 0.49 + 7.29 + 18.49 + 0.09 + 0.49 + 13.69 = 51.54.
- Divide the sum by the number of data points: 51.54 / 7 = 7.36.
- The mean squared deviation is 7.36.
5. Take the square root of the mean squared deviation.
- Calculate the square root of 7.36: √7.36 ≈ 2.7.
Therefore, the standard deviation of the given data set is approximately 2.7 (rounded to the nearest tenth).
To find the standard deviation of a data set, follow these steps:
1. Calculate the mean of the data set.
- Add up all the numbers in the data set: 5 + 9 + 11 + 4 + 8 + 9 + 12 = 58
- Divide the sum by the total number of values: 58 ÷ 7 = 8.29 (rounded to the nearest hundredth)
2. Calculate the deviation of each data point from the mean.
- Take each value and subtract the mean from it. For example, for 5: 5 - 8.29 = -3.29.
3. Square each deviation.
- Square each deviation that was calculated in step 2. For example, (-3.29)² = 10.8241 (rounded to the nearest ten-thousandth).
4. Calculate the mean of the squared deviations.
- Add up all the squared deviations: 10.8241 + 0.0141 + 5.1841 + 21.9441 + 0.1441 + 0.0141 + 15.4841 ≈ 53.6227
- Divide the sum by the total number of values: 53.6227 ÷ 7 ≈ 7.6604 (rounded to the nearest ten-thousandth).
5. Take the square root of the mean of the squared deviations.
- The square root of 7.6604 ≈ 2.7689 (rounded to the nearest ten-thousandth).
Therefore, the standard deviation of the data set 5, 9, 11, 4, 8, 9, 12 is approximately 2.8 (rounded to the nearest tenth).