Question

what is the population variance of these numbers: 25431, 26451, 26536, 26813, 27957, 28824, 29185, 30586, 33531, 33923, 34683, 35623, 37829, 37837, 39391

Answer 1

The population variance of the given data set is approximately

12,586,806.0074.

To calculate the population variance, follow these steps:

Find the mean (average) of the data set.

Subtract the mean from each data point and square the result.

Find the average of these squared differences.

Let's go through the calculations:

Find the mean:

Mean= ∑_i=1xi/n

Mean= 25431+26451+…+39391/15

Mean= 490645/15

Mean=32709.6667

Subtract the mean from each data point and square the result:

(25431−32709.6667)^2 =52468423.5556

(26451−32709.6667)^2 =3895568.5556

…

(39391−32709.6667)^2 =4410839.5556

Find the average of these squared differences:

Variance= ∑_i=1 (xi −Mean)^2/n

​Variance= 52468423.5556+3895568.5556+…+4410839.5556/15

Variance= 188802090.1111/15

Variance=12586806.0074

So, the population variance of the given data set is approximately

12,586,806.0074.