Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
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]
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]
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.