To find the mean and the sample proportion of numbers less than the mean for the given data set, follow these steps:
1. List the Data Set:
The data set consists of the following values:
25.5, 26, 18.2, 15.3, 28.5, 27, 20.7, 20.2, 26.1, 18.2, 21.4, 17.9, 24.3, 22.6, 19.6
2. Calculate the Mean:
The mean (or average) of the data set is determined by summing all the values and then dividing by the number of values.
Sum of the data set:
\( 25.5 + 26 + 18.2 + 15.3 + 28.5 + 27 + 20.7 + 20.2 + 26.1 + 18.2 + 21.4 + 17.9 + 24.3 + 22.6 + 19.6 \)
Count of numbers in the data set:
\( 15 \)
Mean:
[tex]\[
\text{Mean} = \frac{\text{Sum of the values}}{\text{Number of values}}
= \frac{367.5}{15} \approx 22.1
\][/tex]
3. Calculate the Sample Proportion of Numbers Less Than the Mean:
Identify the numbers in the data set that are less than the mean (22.1).
Numbers less than 22.1:
18.2, 15.3, 18.2, 20.7, 20.2, 21.4, 17.9, 19.6
Count of numbers less than 22.1:
\( 8 \)
Sample proportion:
[tex]\[
\text{Sample Proportion} = \frac{\text{Count of numbers less than mean}}{\text{Total count}} \times 100
= \frac{8}{15} \times 100 \approx 53.33\%
\][/tex]
The mean of the data set is \( 22.1 \), and the sample proportion of numbers less than the mean is \( 53.33 \% \).
So, the answers are:
[tex]\[
\text{The mean of the data set is } 22.1 , \text{ and the sample proportion of numbers less than the mean is } 53.33 \% .
\][/tex]
