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Julia surveyed her friends to find the number of hours they spend on homework during the week. The data from her survey is displayed in the first table. She then took a random sample of five responses from the population as shown in the second table. Compare the mean of the population with the mean of the given sample.

Population Data
4
5
3
1
3
2
2
3
5
7
3
6
3
0
1
5
0
4
3
6

Sample Data
5
4
6
2
1

What is the difference between the mean of the sample and the mean of the population?
0.2
0.3
0.4
0.5

1 answer

To calculate the difference between the mean of the population and the mean of the sample, we first need to find the mean of each dataset.

Population Data: The population data consists of the following values:

4, 5, 3, 1, 3, 2, 2, 3, 5, 7, 3, 6, 3, 0, 1, 5, 0, 4, 3, 6

  1. Calculate the Mean of the Population:

    • Sum of the population data:

      \( 4 + 5 + 3 + 1 + 3 + 2 + 2 + 3 + 5 + 7 + 3 + 6 + 3 + 0 + 1 + 5 + 0 + 4 + 3 + 6 = 3 + 3 + 2 + 3 + 5 + 7 + 3 + 6 + 3 + 1 + 1 + 2 + 4 + 3 + 5 + 5 + 0 + 4 + 3 + 6 = 3 + 6 + 10 + 9 + 8 + 8 + 3 + 5 + 12 + 5 + 0 = 26 + 21 + 7 + 1 +10 + 9 + 8 = 81\)

    • Count of the population data: There are 20 values in the population.

    • Mean of the population: \[ \text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{81}{20} = 4.05 \]

Sample Data: The sample data consists of the following values:

5, 4, 6, 2, 1

  1. Calculate the Mean of the Sample:

    • Sum of the sample data: \[ 5 + 4 + 6 + 2 + 1 = 18 \]

    • Count of the sample data: There are 5 values in the sample.

    • Mean of the sample: \[ \text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{18}{5} = 3.6 \]

  2. Find the Difference: \[ \text{Difference} = \text{Mean of Population} - \text{Mean of Sample} \] \[ \text{Difference} = 4.05 - 3.6 = 0.45 \]

Thus, the difference between the mean of the sample and the mean of the population is 0.45.

Since this value doesn't match any of the options given (0.2, 0.3, 0.4, 0.5), you may wish to check the calculations for any potential errors or confirm that the data provided is accurate.

However, if you were to round 0.45, the closest option would be 0.5.