To find the standard deviation, [tex]\(\sigma\)[/tex], of the given data, we need to start with the variance. Here is the detailed, step-by-step solution:
1. Identify the given variance:
- The variance ([tex]\(\sigma^2\)[/tex]) is given as [tex]\(85.3\)[/tex].
2. Calculate the standard deviation:
- The standard deviation ([tex]\(\sigma\)[/tex]) is the square root of the variance ([tex]\(\sigma^2\)[/tex]).
- Therefore, [tex]\(\sigma = \sqrt{85.3}\)[/tex].
3. Calculate the square root of 85.3:
- [tex]\(\sqrt{85.3} \approx 9.235799911215054\)[/tex].
4. Round the standard deviation to the nearest tenth:
- When rounding [tex]\(9.235799911215054\)[/tex] to the nearest tenth, we look at the number in the hundredths place, which is 3. Since 3 is less than 5, we round down.
- Hence, [tex]\(9.235799911215054\)[/tex] rounds to [tex]\(9.2\)[/tex].
Therefore, the standard deviation, [tex]\(\sigma\)[/tex], rounded to the nearest tenth, is [tex]\(9.2\)[/tex].
