Thank you for visiting Find the variance for the given data Round your answer to one more decimal place than the original data Data 18 16 12 2 11. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To find the variance of the given set of data, follow these steps:
1. List the Data:
The data set is: 18, 16, 12, 2, 11.
2. Calculate the Mean:
First, find the mean (average) of the data.
[tex]\[
\text{Mean} = \frac{18 + 16 + 12 + 2 + 11}{5} = \frac{59}{5} = 11.8
\][/tex]
3. Calculate Each Deviation from the Mean:
Subtract the mean from each data point to find the deviation of each value from the mean:
- [tex]\(18 - 11.8 = 6.2\)[/tex]
- [tex]\(16 - 11.8 = 4.2\)[/tex]
- [tex]\(12 - 11.8 = 0.2\)[/tex]
- [tex]\(2 - 11.8 = -9.8\)[/tex]
- [tex]\(11 - 11.8 = -0.8\)[/tex]
4. Square Each Deviation:
Square each of the deviations:
- [tex]\(6.2^2 = 38.44\)[/tex]
- [tex]\(4.2^2 = 17.64\)[/tex]
- [tex]\(0.2^2 = 0.04\)[/tex]
- [tex]\((-9.8)^2 = 96.04\)[/tex]
- [tex]\((-0.8)^2 = 0.64\)[/tex]
5. Calculate the Variance:
The variance is the average of these squared deviations. Since this is sample data, use [tex]\(n-1\)[/tex] (where [tex]\(n\)[/tex] is the number of data points) for the calculation.
[tex]\[
\text{Variance} = \frac{38.44 + 17.64 + 0.04 + 96.04 + 0.64}{5 - 1} = \frac{152.8}{4} = 38.2
\][/tex]
6. Rounding the Result:
Since all original data had no decimal places, round the variance to one decimal place.
[tex]\[
\text{Variance (rounded)} = 38.2
\][/tex]
Therefore, the variance of the data set is [tex]\(38.2\)[/tex].
1. List the Data:
The data set is: 18, 16, 12, 2, 11.
2. Calculate the Mean:
First, find the mean (average) of the data.
[tex]\[
\text{Mean} = \frac{18 + 16 + 12 + 2 + 11}{5} = \frac{59}{5} = 11.8
\][/tex]
3. Calculate Each Deviation from the Mean:
Subtract the mean from each data point to find the deviation of each value from the mean:
- [tex]\(18 - 11.8 = 6.2\)[/tex]
- [tex]\(16 - 11.8 = 4.2\)[/tex]
- [tex]\(12 - 11.8 = 0.2\)[/tex]
- [tex]\(2 - 11.8 = -9.8\)[/tex]
- [tex]\(11 - 11.8 = -0.8\)[/tex]
4. Square Each Deviation:
Square each of the deviations:
- [tex]\(6.2^2 = 38.44\)[/tex]
- [tex]\(4.2^2 = 17.64\)[/tex]
- [tex]\(0.2^2 = 0.04\)[/tex]
- [tex]\((-9.8)^2 = 96.04\)[/tex]
- [tex]\((-0.8)^2 = 0.64\)[/tex]
5. Calculate the Variance:
The variance is the average of these squared deviations. Since this is sample data, use [tex]\(n-1\)[/tex] (where [tex]\(n\)[/tex] is the number of data points) for the calculation.
[tex]\[
\text{Variance} = \frac{38.44 + 17.64 + 0.04 + 96.04 + 0.64}{5 - 1} = \frac{152.8}{4} = 38.2
\][/tex]
6. Rounding the Result:
Since all original data had no decimal places, round the variance to one decimal place.
[tex]\[
\text{Variance (rounded)} = 38.2
\][/tex]
Therefore, the variance of the data set is [tex]\(38.2\)[/tex].
Thank you for reading the article Find the variance for the given data Round your answer to one more decimal place than the original data Data 18 16 12 2 11. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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