What is the standard deviation for the following set of scores: 10, 15, 12, 18, 19, 16, 12?
Group of answer choices

17.78

11.29

6.47

3.36

To calculate the **standard deviation** for the given set of scores, we follow these steps:

### Scores: 10, 15, 12, 18, 19, 16, 12

#### Step 1: Calculate the mean (average)
\[
\text{Mean} = \frac{\sum \text{scores}}{n} = \frac{10 + 15 + 12 + 18 + 19 + 16 + 12}{7} = \frac{102}{7} \approx 14.57
\]

#### Step 2: Calculate each score's deviation from the mean
For each score, subtract the mean and square the result:

\[
(10 - 14.57)^2 \approx (-4.57)^2 = 20.89
\]
\[
(15 - 14.57)^2 \approx (0.43)^2 = 0.18
\]
\[
(12 - 14.57)^2 \approx (-2.57)^2 = 6.60
\]
\[
(18 - 14.57)^2 \approx (3.43)^2 = 11.76
\]
\[
(19 - 14.57)^2 \approx (4.43)^2 = 19.62
\]
\[
(16 - 14.57)^2 \approx (1.43)^2 = 2.04
\]
\[
(12 - 14.57)^2 \approx (-2.57)^2 = 6.60
\]

#### Step 3: Calculate the variance
The variance is the average of the squared deviations:
\[
\text{Variance} = \frac{\sum (\text{deviation}^2)}{n} = \frac{20.89 + 0.18 + 6.60 + 11.76 + 19.62 + 2.04 + 6.60}{7} = \frac{67.69}{7} \approx 9.67
\]

#### Step 4: Calculate the standard deviation
The standard deviation is the square root of the variance:
\[
\text{Standard deviation} = \sqrt{9.67} \approx 3.11
\]

### Answer
The closest answer to our calculated result is **3.36**, which is the correct choice from the options.

### Do you want more details or have any questions?

### Related Questions:
1. What is the difference between standard deviation and variance?
2. How does sample size affect standard deviation?
3. Why do we square deviations in standard deviation calculations?
4. How do you interpret a high vs. low standard deviation?
5. Can you calculate the standard deviation for a different set of numbers?

**Tip:** Always remember that standard deviation provides insight into the **spread** or **dispersion** of your data values.

What is the standard deviation for the following set of scores: 10, 15, 12, 18, 19, 16, 12?

Discover how to calculate the standard deviation for the set of scores: 10, 15, 12, 18, 19, 16, 12. This problem includes calculating the mean, variance, and standard deviation with step-by-step instructions. Ideal for students in Grades 9-12 learning about statistical concepts.

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