What is the population variance of the data set 125, 234, 152, 340, 204?

To assess the population variance of the given dataset (125, 234, 152, 340, 204), it's essential first to understand what population variance is. Population variance measures the dispersion of a set of data points, indicating how far each data point is from the population mean, squared.

To calculate the population variance, follow these steps:

1. Calculate the Mean:

• Add all the numbers together:

( 125 + 234 + 152 + 340 + 204 = 1055 )

• Divide by the number of data points (5 in this case):

( \text{Mean} = \frac{1055}{5} = 211 )

2. Calculate Each Deviation from the Mean:

• Subtract the mean from each data point:

• ( 125 - 211 = -86 )

• ( 234 - 211 = 23 )

• ( 152 - 211 = -59 )

• ( 340 - 211 = 129 )

• ( 204 - 211 = -7 )

3. Square Each Deviation:

• ( (-86