Find the Standard Deviation of (Rs.) 7, 9, 16, 24, 26.

To calculate the standard deviation of a set of numbers, we follow these steps:

### Step 1: Find the Mean (Average)
First, we calculate the mean (average) of the numbers.

Given numbers: \(7, 9, 16, 24, 26\)

\[
\text{Mean} (\mu) = \frac{7 + 9 + 16 + 24 + 26}{5} = \frac{82}{5} = 16.4
\]

### Step 2: Find the Variance
Variance is the average of the squared differences from the Mean.

\[
\text{Variance} (\sigma^2) = \frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2
\]

Where \(x_i\) represents each value in the dataset and \(n\) is the number of values.

Now, calculate each squared difference:

\[
\begin{aligned}
(7 - 16.4)^2 & = (-9.4)^2 = 88.36, \\
(9 - 16.4)^2 & = (-7.4)^2 = 54.76, \\
(16 - 16.4)^2 & = (-0.4)^2 = 0.16, \\
(24 - 16.4)^2 & = (7.6)^2 = 57.76, \\
(26 - 16.4)^2 & = (9.6)^2 = 92.16.
\end{aligned}
\]

Now, sum these squared differences:

\[
88.36 + 54.76 + 0.16 + 57.76 + 92.16 = 293.2
\]

Finally, divide by the number of data points (n = 5):

\[
\text{Variance} (\sigma^2) = \frac{293.2}{5} = 58.64
\]

### Step 3: Find the Standard Deviation
The standard deviation is the square root of the variance:

\[
\sigma = \sqrt{58.64} \approx 7.65
\]

### Final Answer
The standard deviation of the given numbers is approximately \( \sigma \approx 7.65 \) Rs.

Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:
1. What is the difference between variance and standard deviation?
2. How does standard deviation help in understanding data dispersion?
3. How would the standard deviation change if all values in the dataset increased by the same amount?
4. Can standard deviation be zero, and what does it imply?
5. What is the relationship between standard deviation and the normal distribution?

**Tip:** Standard deviation is a useful measure to understand how spread out the values in a dataset are. A larger standard deviation indicates more variability among the data points.

Learn how to calculate the standard deviation of the numbers 7, 9, 16, 24, 26 with a step-by-step solution. This problem covers key statistical concepts, including variance calculation and standard deviation. Suitable for high school students.

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