Question

Find the standard deviation of the following dataset: (2,7,5,2).
(3)
SELECT THE CORRECT ANSWER
V6
6
2
Impossible to calculate
None of the given answers

Answer 1

To find the standard deviation of the dataset \( (2, 7, 5, 2) \), we can follow these steps:

1. **Calculate the mean of the dataset**:
\[
\text{Mean} = \frac{(2 + 7 + 5 + 2)}{4} = \frac{16}{4} = 4
\]

2. **Calculate the squared deviations from the mean**:
- For 2: \((2 - 4)^2 = (-2)^2 = 4\)
- For 7: \((7 - 4)^2 = (3)^2 = 9\)
- For 5: \((5 - 4)^2 = (1)^2 = 1\)
- For 2: \((2 - 4)^2 = (-2)^2 = 4\)

The squared deviations are \(4, 9, 1, 4\).

3. **Calculate the variance**:
\[
\text{Variance} = \frac{(4 + 9 + 1 + 4)}{4} = \frac{18}{4} = 4.5
\]

4. **Calculate the standard deviation**:
\[
\text{Standard Deviation} = \sqrt{4.5} \approx 2.1213
\]

Now let's evaluate the options given:

- \(V6\)
- \(6\)
- \(2\)
- \(Impossible to calculate\)
- \(None of the given answers\)

The standard deviation approximately equals \(2.1213\), which does not exactly match any of the provided options.

Therefore, the correct answer is **None of the given answers**.