Population Variance Calculation

B

Population variance = (Sum of squared deviation from the mean)/N. the mean is 28. Population variance = (100 + 4 + 225 + 169 + 36)/5 = 534/5 = 106.8 xx-mean(x-mean)^2

3810100

26-24

13-15225

4113169

22-636

To calculate the population variance, you need to follow these steps:

1. Find the mean (average) of the data set.

   • Add up all the ages: 38 + 26 + 13 + 41 + 22 = 140.
   • Divide the sum by the number of data points (in this case, 5): 140 / 5 = 28.
   • The mean age is 28.

2. Calculate the deviation from the mean for each data point.

   • For each age, subtract the mean (28) from the age itself.
     • Deviation for 38: 38 - 28 = 10
     • Deviation for 26: 26 - 28 = -2
     • Deviation for 13: 13 - 28 = -15
     • Deviation for 41: 41 - 28 = 13
     • Deviation for 22: 22 - 28 = -6

3. Square each deviation.

   • Square each deviation you calculated in the previous step.
     • Squared deviation for 10: 10^2 = 100
     • Squared deviation for -2: (-2)^2 = 4
     • Squared deviation for -15: (-15)^2 = 225
     • Squared deviation for 13: 13^2 = 169
     • Squared deviation for -6: (-6)^2 = 36

4. Find the sum of squared deviations.

   • Add up all the squared deviations.
     • Sum of squared deviations = 100 + 4 + 225 + 169 + 36 = 534.

5. Divide the sum of squared deviations by the number of data points (population size).

   • Divide the sum of squared deviations (534) by the number of data points (5).
   • Population variance = 534 / 5 = 106.8.