https://file.aiquickdraw.com/mathbot/file/1727310250047u9bfm58a.jpg

The equation in the image corresponds to the standard deviation formula, particularly for a sample. Here's how to solve it step-by-step:

The formula shown is:

\[
\Delta X = \frac{1}{N} \sqrt{\frac{N \sum X_i^2 - \left( \sum X_i \right)^2}{N-1}}
\]

In the second part, values are substituted:

\[
= \frac{1}{5} \sqrt{\frac{5 \cdot 1183.40 - (76.27)^2}{5-1}}
\]

Now let's compute it step-by-step:

1. **Multiply \( N \) by \( \sum X_i^2 \):**

\[
5 \cdot 1183.40 = 5917
\]

2. **Square the sum of \( X_i \):**

\[
(76.27)^2 = 5817.8129
\]

3. **Subtract the squared sum from the previous result:**

\[
5917 - 5817.8129 = 99.1871
\]

4. **Divide the result by \( N - 1 \):**

\[
\frac{99.1871}{4} = 24.796775
\]

5. **Take the square root:**

\[
\sqrt{24.796775} \approx 4.9796
\]

6. **Finally, divide by \( N \) (which is 5):**

\[
\frac{4.9796}{5} = 0.99592
\]

Therefore, the result is approximately **0.996**.

Would you like more details or clarification on any of these steps?

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Here are 5 related questions to extend your understanding:

1. What is the difference between population standard deviation and sample standard deviation?
2. How is the variance related to standard deviation?
3. Why do we divide by \( N-1 \) in the sample standard deviation formula?
4. Can you compute the mean for the same data set based on the given sums?
5. What is the significance of using standard deviation in data analysis?

**Tip:** Always double-check the distinction between \( N \) (population size) and \( N-1 \) (sample size) in your formulas.

Learn how to compute the sample standard deviation using ΣXi and ΣXi² values in this step-by-step solution. The formula includes a division by N-1 to account for sample data, with results calculated based on provided sums.

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