Find the mean, variance and standard deviation for the following data
6, 12, 6, 8, 10, 8, 12, 8, 14, 16
To find the mean, variance, and standard deviation of a set of data, follow these steps:
1. Calculate the mean:
- Add up all the numbers in the data set: 6 + 12 + 6 + 8 + 10 + 8 + 12 + 8 + 14 + 16 = 100.
- Divide the sum by the number of data points: 100 / 10 = 10.
- Therefore, the mean of the given data set is 10.
2. Calculate the variance:
- Subtract the mean from each data point and square the result:
(6 - 10)^2 + (12 - 10)^2 + (6 - 10)^2 + (8 - 10)^2 + (10 - 10)^2 + (8 - 10)^2 + (12 - 10)^2 + (8 - 10)^2 + (14 - 10)^2 + (16 - 10)^2 = 68.
- Divide the sum of squared differences by the number of data points: 68 / 10 = 6.8.
- Therefore, the variance of the given data set is 6.8.
3. Calculate the standard deviation:
- Take the square root of the variance: √6.8 ≈ 2.61.
- Therefore, the standard deviation of the given data set is approximately 2.61.
So, the mean is 10, the variance is 6.8, and the standard deviation is approximately 2.61 for the provided data set.