We are given the data set: $7, 6, 4, 5, 5, 2, 1, 2, 3$.

1. Mean

The mean (average) is calculated by summing all the values and dividing by the number of values.

$\text{Mean} = \frac{7 + 6 + 4 + 5 + 5 + 2 + 1 + 2 + 3}{9} = \frac{35}{9} \approx 3.89$

2. Standard Deviation (SD)

First, we need to find the variance:

• Step 1: Calculate the deviations from the mean for each value.
• Step 2: Square those deviations.
• Step 3: Find the average of those squared deviations (this is the variance).
• Step 4: Take the square root of the variance to get the standard deviation.

Let me calculate this:

$\text{Variance} = \frac{(7 - 3.89)^2 + (6 - 3.89)^2 + (4 - 3.89)^2 + (5 - 3.89)^2 + (5 - 3.89)^2 + (2 - 3.89)^2 + (1 - 3.89)^2 + (2 - 3.89)^2 + (3 - 3.89)^2}{9}$

Now, I'll compute the result:

$\text{Variance} \approx 3.43$

$\text{Standard Deviation} \approx \sqrt{3.43} \approx 1.85$

3. Range

The range is the difference between the maximum and minimum values:

$\text{Range} = 7 - 1 = 6$

Summary:

• Mean: $\approx 3.89$
• Standard Deviation: $\approx 1.85$
• Range: $6$

Would you like further details or have any questions?

5 Related Questions:

1. How is variance related to standard deviation?
2. What is the difference between population standard deviation and sample standard deviation?
3. How does the range affect the spread of data?
4. Can standard deviation be negative?
5. What happens to the mean if we add more values to the dataset?

Tip:

For a small dataset, the range can provide quick insight into data spread, but standard deviation gives a more comprehensive understanding.