Question
If variance of the data set is 6 , what is the standard deviation of the data set? 36.00 12.00 3.00 2.45
Ask by Ramos Christensen. in South Africa
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The standard deviation is 2.45.
Solution
To find the standard deviation of a data set when the variance is given, we can use the relationship between variance and standard deviation. The standard deviation (SD) is the square root of the variance (Var).
Given:
- Variance (Var) = 6
The formula to calculate standard deviation is:
\[
SD = \sqrt{Var}
\]
Now, let's calculate the standard deviation:
\[
SD = \sqrt{6}
\]
Now, I will calculate the square root of 6.
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{6}\)
The standard deviation is calculated as:
\[
SD = \sqrt{6} \approx 2.44949
\]
Rounding this to two decimal places gives us approximately \(2.45\).
Thus, the standard deviation of the data set is **2.45**.
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Simplify this solution The Deep Dive
The standard deviation is simply the square root of the variance. So in this case, if the variance of the data set is 6, you would calculate the standard deviation as follows: √6, which is approximately 2.45. Hence, the correct answer from the options provided is 2.45! Understanding the relationship between variance and standard deviation is crucial in statistics because it allows researchers and analysts to gauge the spread of data more intuitively. While variance gives a squared measure of dispersion, standard deviation translates that into the same units as the original data, making it more relatable and easier to apply in real-world scenarios.
