Final answer:
The population variance of the three ages (1, 4, and 10) is calculated as 14. The calculation differs for sample variance which uses n-1 as the denominator.
Step-by-step explanation:
Calculating Population Variance
To calculate the population variance of the ages of the children, we first need to find the mean (average) of the population. We then subtract the mean from each age to find the deviations, square these deviations, and find the average of the squared deviations.
The population variance is different from the sample variance, where we typically divide by n-1 instead of n. This adjustment for the sample variance is done because using n-1 provides an unbiased estimator for the population variance as it compensates for the fact that we are estimating using a sample instead of the full population.
The mean age of the children is (1 + 4 + 10) / 3 = 5. Deviations are (1-5), (4-5), and (10-5), which are -4, -1, and 5, respectively. Squaring these gives 16, 1, and 25. The population variance is (16 + 1 + 25) / 3, which equals 14 (rounded to three decimal places as needed).
To find the value of the population variance, we first calculate the mean of the ages of the children. The mean is (1+4+10)/3 = 5.
Next, we calculate the deviation from the mean for each age: (1-5)^2 = 16, (4-5)^2 = 1, and (10-5)^2 = 25. Taking the average of these squared deviations gives us (16+1+25)/3 = 14.667. Therefore, the value of the population variance is 14.667 (rounded to three decimal places).