Question

Calculate Sample Variance for the following data collection: 10, 11, 12, 13, 14,18.

Answer 1

To calculate the sample variance, find the mean of the data set and then subtract the mean from each data point, square the result, add up all the squared differences, and divide by the number of data points minus one.

Step-by-step explanation:

To calculate the sample variance, follow these steps:

1. Find the mean of the data set. In this case, the mean is (10 + 11 + 12 + 13 + 14 + 18) / 6 = 78 / 6 = 13.
2. Subtract the mean from each data point and square the result. For example, (10 - 13)^2 = 9, (11 - 13)^2 = 4, and so on.
3. Add up all the squared differences. In this case, 9 + 4 + 1 + 0 + 1 + 25 = 40.
4. Divide the sum by the number of data points minus one. In this case, 40 / (6 - 1) = 40 / 5 = 8.

Therefore, the sample variance for the given data set is 8.

Answer 2

The Variance of a set of data is defined as the average of the square of the deviation from the mean.

The first step is to calculate the mean of the data.

`(10+11+12+13+14+18)/(6)=13`

Now we take the difference from the mean, square it, and then average the result.

`((10-13)^2+(11-13^2)+(12-13)^2+(13-13)^2+(14-13)^2+(18-13)^2)/(6)`
`\Rightarrow(9+4+1+0+1+25)/(6)`
`\Rightarrow6.67`

Hence, the variance of the data is 6.7 (rounded to the nearest tenth)