Ask the standard deviations of the scores 6,7,8,9 and 10

To find the standard deviation of the scores \(6, 7, 8, 9, 10\), we follow these steps:

### Step 1: Calculate the Mean
First, find the mean (average) of the data set.

\[
\text{Mean} = \frac{6 + 7 + 8 + 9 + 10}{5} = \frac{40}{5} = 8
\]

### Step 2: Calculate Each Score's Deviation from the Mean
Next, subtract the mean from each score:

- \(6 - 8 = -2\)
- \(7 - 8 = -1\)
- \(8 - 8 = 0\)
- \(9 - 8 = 1\)
- \(10 - 8 = 2\)

### Step 3: Square Each Deviation
Now, square each deviation:

- \((-2)^2 = 4\)
- \((-1)^2 = 1\)
- \(0^2 = 0\)
- \(1^2 = 1\)
- \(2^2 = 4\)

### Step 4: Find the Mean of These Squared Deviations
Calculate the average of the squared deviations:

\[
\text{Variance} = \frac{4 + 1 + 0 + 1 + 4}{5} = \frac{10}{5} = 2
\]

### Step 5: Take the Square Root of the Variance
Finally, the standard deviation is the square root of the variance:

\[
\text{Standard Deviation} = \sqrt{2} \approx 1.41
\]

So, the standard deviation of the scores \(6, 7, 8, 9, 10\) is approximately **1.41**.

Would you like more details or have any questions about this? 

Here are some related questions you might consider:
1. How would the standard deviation change if all scores increased by 2?
2. What is the significance of a low or high standard deviation?
3. How would you compute the variance for the same data set?
4. How does the standard deviation relate to the range of data?
5. How do you interpret the standard deviation in the context of normal distribution?

**Tip:** When the standard deviation is small, the data points are close to the mean, indicating low variability in the data set.

Learn how to calculate the standard deviation of scores 6, 7, 8, 9, and 10 with a step-by-step solution. This problem covers key statistical concepts, including mean, variance, and standard deviation. Suitable for students in Grades 9-12.

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