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

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

• A. 5,619.20
• B. 28,096
• C. 74.96
• D. 3,760

Answer: (A)

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

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