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.

Question

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

Answer 1

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

1. Calculate the mean of the population:

Population data: 4, 5, 3, 1, 3, 2, 2, 3, 5, 7, 3, 6, 3, 0, 1, 5, 0, 4, 3, 6

Sum of population data = 4 + 5 + 3 + 1 + 3 + 2 + 2 + 3 + 5 + 7 + 3 + 6 + 3 + 0 + 1 + 5 + 0 + 4 + 3 + 6 = 66

Number of data points in the population = 20

Mean of the population = Sum of population data / Number of data points = 66 / 20 = 3.3

2. Calculate the mean of the sample:

Sample data: 5, 4, 6, 2, 1

Sum of sample data = 5 + 4 + 6 + 2 + 1 = 18

Number of data points in the sample = 5

Mean of the sample = Sum of sample data / Number of data points = 18 / 5 = 3.6

3. Calculate the difference between the mean of the sample and the mean of the population:

Difference = Mean of the sample - Mean of the population = 3.6 - 3.3 = 0.3

Thus, the difference between the mean of the sample and the mean of the population is 0.3.

So the answer is 0.3.