The data below shows the scores of 8 students in a test:-

 

8, 6, 3, 5, 3, 4, 2,9

Find the standard deviation. Round your answer to 2 decimal places. 



To calculate the standard deviation of the given data set, follow these steps:

### Data Set: 
\[ 8, 6, 3, 5, 3, 4, 2, 9 \]

### Step 1: Calculate the Mean
The mean (\(\mu\)) is the sum of all the data points divided by the number of data points.

\[
\mu = \frac{8 + 6 + 3 + 5 + 3 + 4 + 2 + 9}{8} = \frac{40}{8} = 5
\]

### Step 2: Find the Differences from the Mean
Subtract the mean from each data point to get the deviation of each point:

\[
\text{Deviations}: (8 - 5), (6 - 5), (3 - 5), (5 - 5), (3 - 5), (4 - 5), (2 - 5), (9 - 5)
\]
\[
= 3, 1, -2, 0, -2, -1, -3, 4
\]

### Step 3: Square Each Deviation
Now, square each of these deviations:

\[
(3^2), (1^2), (-2^2), (0^2), (-2^2), (-1^2), (-3^2), (4^2)
\]
\[
= 9, 1, 4, 0, 4, 1, 9, 16
\]

### Step 4: Calculate the Mean of the Squared Deviations (Variance)
Find the mean of these squared deviations:

\[
\text{Variance} = \frac{9 + 1 + 4 + 0 + 4 + 1 + 9 + 16}{8} = \frac{44}{8} = 5.5
\]

### Step 5: Take the Square Root (Standard Deviation)
The standard deviation (\(\sigma\)) is the square root of the variance:

\[
\sigma = \sqrt{5.5} \approx 2.35
\]

### Answer:
The standard deviation of the data set is approximately **2.35**.

---

Would you like more details on this process or have any questions?

Here are some additional questions related to this topic:

1. How does the standard deviation change if you add more data points?
2. What is the difference between standard deviation and variance?
3. How does the range of a data set relate to its standard deviation?
4. What does a low standard deviation indicate about a data set?
5. How would the standard deviation change if all the scores were increased by the same amount?

**Tip:** The standard deviation measures the spread of data around the mean. The larger the value, the more spread out the data points are from the mean.

The data below shows the scores of 8 students in a test: 8, 6, 3, 5, 3, 4, 2, 9. Find the standard deviation. Round your answer to 2 decimal places.

Learn how to calculate the standard deviation of a data set: 8, 6, 3, 5, 3, 4, 2, 9. This solution covers key statistical concepts like mean, variance, and standard deviation with a detailed step-by-step guide. Suitable for students in Grades 9-11.

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