To calculate the standard deviation of the data, we'll follow these steps:

1. **Calculate the mean \(\mu_X\)** (already found as 1.607).

2. **Calculate each squared deviation from the mean**, which is \((x_i - \mu_X)^2\), and then multiply by the corresponding frequency \(f_i\).

3. **Sum the squared deviations**.

4. **Divide by the total number of observations** \(N\) to find the variance.

5. **Take the square root of the variance** to find the standard deviation.

Let's proceed with the calculation:

### Step 1: Squared Deviations

\[
(x_i - \mu_X)^2
\]
\[
\begin{array}{|c|c|c|c|}
\hline
x_i & f_i & (x_i - \mu_X) & (x_i - \mu_X)^2 \times f_i \\
\hline
0 & 24 & 0 - 1.607 = -1.607 & (-1.607)^2 \times 24 \approx 62.020 \\
1 & 434 & 1 - 1.607 = -0.607 & (-0.607)^2 \times 434 \approx 159.823 \\
2 & 261 & 2 - 1.607 = 0.393 & (0.393)^2 \times 261 \approx 40.237 \\
3 & 79 & 3 - 1.607 = 1.393 & (1.393)^2 \times 79 \approx 153.476 \\
4 & 19 & 4 - 1.607 = 2.393 & (2.393)^2 \times 19 \approx 108.948 \\
5 & 13 & 5 - 1.607 = 3.393 & (3.393)^2 \times 13 \approx 149.497 \\
\hline
\end{array}
\]

### Step 2: Sum the Squared Deviations

Sum of squared deviations:
\[
62.020 + 159.823 + 40.237 + 153.476 + 108.948 + 149.497 \approx 674.001
\]

### Step 3: Calculate the Variance

\[
\text{Variance} = \frac{674.001}{830} \approx 0.812
\]

### Step 4: Calculate the Standard Deviation

\[
\text{Standard Deviation} = \sqrt{0.812} \approx 0.901
\]

So, the standard deviation of the dataset is approximately **0.901**.

Would you like further details or have any questions?

---

Here are 8 related questions for further exploration:

1. How does the standard deviation help in understanding the distribution of the data?
2. What would the standard deviation be if all values were closer to the mean?
3. Can you calculate the variance manually from the standard deviation?
4. How does increasing the frequency of one of the days affect the standard deviation?
5. What is the interpretation of a low standard deviation in this context?
6. How would the standard deviation change if the highest frequency day (1 day) had an even higher frequency?
7. Can you plot the data distribution and analyze it visually?
8. How does the standard deviation compare to the mean in this dataset?

**Tip:** The standard deviation is a measure of spread that tells us how much the values in a dataset typically differ from the mean. A smaller standard deviation means that the data points are closer to the mean.

Learn how to calculate the standard deviation of a dataset with a step-by-step guide and example. Understand the variance and standard deviation formulas applied to real data. Suitable for undergraduate level and beyond.

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