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Type the correct answer in the box. Use numerals instead of words. For this question, any non-integer answers should be entered as decimals, rounded to the hundredths place.

Consider this data set:

\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|c|}{Data Set} \\
\hline 25.5 & 26 & 18.2 \\
\hline 15.3 & 28.5 & 27 \\
\hline 20.7 & 20.2 & 26.1 \\
\hline 18.2 & 21.4 & 17.9 \\
\hline 24.3 & 22.6 & 19.6 \\
\hline
\end{tabular}

The mean of the data set is [tex]$\square$[/tex] , and the sample proportion of numbers less than the mean is [tex]$\square$[/tex] \%.



Answer :

GinnyAnswer
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]

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