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To compute the **mean** and **standard deviation** of the sample provided:

Sample: \( 11, 14, 18, 20, 21, 24, 27 \)

### 1. **Mean**:
The mean is calculated by summing all the values and dividing by the number of values.

\[
\text{Mean} = \frac{11 + 14 + 18 + 20 + 21 + 24 + 27}{7} = \frac{135}{7} \approx 19.29
\]

### 2. **Standard Deviation**:
For the standard deviation, we first need to compute the variance. The steps are:

- Subtract the mean from each data point, square the result.
- Sum these squared differences.
- Divide by \( n-1 \) (for sample standard deviation).
- Take the square root of the variance.

**Step-by-step Calculation:**

1. Mean = 19.29
2. Subtract the mean and square the result for each value:
   \[
   (11 - 19.29)^2 = 68.72, \quad
   (14 - 19.29)^2 = 27.97, \quad
   (18 - 19.29)^2 = 1.66
   \]
   \[
   (20 - 19.29)^2 = 0.50, \quad
   (21 - 19.29)^2 = 2.93, \quad
   (24 - 19.29)^2 = 22.23, \quad
   (27 - 19.29)^2 = 59.37
   \]

3. Sum of squared differences:
   \[
   68.72 + 27.97 + 1.66 + 0.50 + 2.93 + 22.23 + 59.37 = 183.38
   \]

4. Divide by \( n-1 = 6 \):
   \[
   \frac{183.38}{6} \approx 30.56
   \]

5. Square root of the variance (standard deviation):
   \[
   \sqrt{30.56} \approx 5.53
   \]

### Final Results:
- Mean = **19.29**
- Standard Deviation = **5.53**

Would you like further clarification or details? 

Here are 5 related questions you might explore:
1. How is the variance related to the standard deviation?
2. How would these calculations change if this were a population instead of a sample?
3. What is the significance of using \( n-1 \) instead of \( n \) in the standard deviation formula?
4. How would you compute the median of this dataset?
5. Can the mean and standard deviation provide insight into the distribution of the data?

**Tip:** Always use \( n-1 \) in the denominator when computing the standard deviation for a sample to avoid underestimating variability.

Compute the mean and standard deviation for the sample below, rounding each to the nearest hundredth: 11, 14, 18, 20, 21, 24, 27

Learn how to calculate the mean and standard deviation for the sample: 11, 14, 18, 20, 21, 24, 27. This problem demonstrates the use of core statistical concepts like mean, variance, and standard deviation, suitable for Grades 9-12.

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