Question

Calculate the variance of the following sample of ages: 2, 3, 4, 1, 8, 9.

Answer 1

To calculate the variance of a sample, first calculate the mean. Then, calculate the deviation for each age and square each deviation. Next, sum the squared deviations and divide by the number of ages minus 1. The variance of the given sample of ages is 10.7.

Step-by-step explanation:

To calculate the variance of a sample, follow these steps:

1. Calculate the mean of the sample by adding up all the ages and dividing by the number of ages. In this case, the mean is 4.5.
2. Calculate the deviation for each age by subtracting the mean from each age. The deviations are: -2.5, -1.5, -0.5, -3.5, 3.5, 4.5.
3. Square each deviation. The squared deviations are: 6.25, 2.25, 0.25, 12.25, 12.25, 20.25.
4. Calculate the sum of the squared deviations, which is 53.5.
5. Divide the sum of squared deviations by the number of ages minus 1. Since there are 6 ages, the variance is 53.5 / (6-1) = 10.7.

So, the variance of the given sample of ages is 10.7.