Question

jan wants to find the number of hours they spend on homework during the week. she took a random sample of five responses from the population. the first table displays the sample data. the second table compares the mean of the given sample with the mean of the population. what is the difference between the mean of the sample and the mean of the population?
population data

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

sample data
|1|
|2|
|6|
|4|
|5|
0.2 0.3 0.4

Explanation:

Step1: Calculate sample mean

The sample data is \(1,2,6,4,5\). The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 5\), \(\sum_{i=1}^{5}x_{i}=1 + 2+6 + 4+5=18\). So the sample mean \(\bar{x}=\frac{18}{5}=3.6\).

Step2: Calculate population mean

The population data has \(n = 20\) values. \(\sum_{i = 1}^{20}x_{i}=3+7 + 1+6+1+5+0+3+3+3+3+4+5+2+6+0+4+2+3+5 = 70\). The population mean \(\mu=\frac{70}{20}=3.5\).

Step3: Calculate the difference

The difference between the sample - mean and the population mean is \(|\bar{x}-\mu|=|3.6 - 3.5|=0.1\).

Answer:

0.1