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Answer :
To find the standard deviation, [tex]\(\sigma\)[/tex], of the given data set, we can follow these steps:
1. Understand the Terms:
- The mean ([tex]\(\bar{x}\)[/tex]) of the data is given as 205.
- The variance ([tex]\(\sigma^2\)[/tex]) is provided as 366.3.
2. Standard Deviation Formula:
- The standard deviation is the square root of the variance. This is because variance measures how far each number in the set is from the mean and how far the numbers are spread out. The standard deviation gives us an average distance from the mean.
3. Calculate the Standard Deviation:
- To find the standard deviation, take the square root of the variance:
[tex]\[
\sigma = \sqrt{\sigma^2}
\][/tex]
- Plug in the given variance value:
[tex]\[
\sigma = \sqrt{366.3}
\][/tex]
- Calculate the square root:
[tex]\[
\sigma \approx 19.14
\][/tex]
Therefore, the standard deviation of the data is approximately 19.14.
1. Understand the Terms:
- The mean ([tex]\(\bar{x}\)[/tex]) of the data is given as 205.
- The variance ([tex]\(\sigma^2\)[/tex]) is provided as 366.3.
2. Standard Deviation Formula:
- The standard deviation is the square root of the variance. This is because variance measures how far each number in the set is from the mean and how far the numbers are spread out. The standard deviation gives us an average distance from the mean.
3. Calculate the Standard Deviation:
- To find the standard deviation, take the square root of the variance:
[tex]\[
\sigma = \sqrt{\sigma^2}
\][/tex]
- Plug in the given variance value:
[tex]\[
\sigma = \sqrt{366.3}
\][/tex]
- Calculate the square root:
[tex]\[
\sigma \approx 19.14
\][/tex]
Therefore, the standard deviation of the data is approximately 19.14.
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