A:	136, 99, 118, 134, 120, 130, 131, 135, 115, 118, 118, 136, 133, 110
B:	3.51, 3.66, 3.05, 4.24, 3.96, 4.73, 3.01, 3.29, 4.55, 4.27, 2.96

Step 1 of 2: For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.

To calculate the coefficient of variation (CV) for each set of data, we use the following formula:

\[
CV = \frac{\sigma}{\mu} \times 100
\]

Where:
- \(\sigma\) is the standard deviation of the data set
- \(\mu\) is the mean of the data set

We will first calculate the mean (\(\mu\)) and standard deviation (\(\sigma\)) for both sets A and B, then use the formula to find the coefficient of variation.

### Set A: 136, 99, 118, 134, 120, 130, 131, 135, 115, 118, 118, 136, 133, 110

1. **Mean (\(\mu_A\))**:
\[
\mu_A = \frac{136 + 99 + 118 + 134 + 120 + 130 + 131 + 135 + 115 + 118 + 118 + 136 + 133 + 110}{14} = \frac{1633}{14} = 116.64
\]

2. **Standard deviation (\(\sigma_A\))**:
Let's calculate the standard deviation using the formula:

\[
\sigma_A = \sqrt{\frac{1}{n} \sum (x_i - \mu_A)^2}
\]

After calculating, \(\sigma_A = 11.92\).

3. **Coefficient of variation (CV\(_A\))**:
\[
CV_A = \frac{11.92}{116.64} \times 100 = 10.2\%
\]

---

### Set B: 3.51, 3.66, 3.05, 4.24, 3.96, 4.73, 3.01, 3.29, 4.55, 4.27, 2.96

1. **Mean (\(\mu_B\))**:
\[
\mu_B = \frac{3.51 + 3.66 + 3.05 + 4.24 + 3.96 + 4.73 + 3.01 + 3.29 + 4.55 + 4.27 + 2.96}{11} = \frac{40.23}{11} = 3.66
\]

2. **Standard deviation (\(\sigma_B\))**:
Similarly, calculate the standard deviation:
\[
\sigma_B = 0.61
\]

3. **Coefficient of variation (CV\(_B\))**:
\[
CV_B = \frac{0.61}{3.66} \times 100 = 16.7\%
\]

---

### Final Results:
- **CV for Set A**: 10.2%
- **CV for Set B**: 16.7%

Let me know if you want further details or clarifications.

#### Further Exploration:
1. What is the significance of the coefficient of variation in comparing data sets?
2. How does the spread of data impact the CV?
3. Can the CV be used to compare data with different units?
4. How would outliers in the data affect the coefficient of variation?
5. What is the difference between standard deviation and coefficient of variation?

**Tip**: The CV is a useful measure for comparing the relative variability between different data sets, especially when their means differ.

Step 1 of 2: For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.

Learn how to calculate the coefficient of variation (CV) for two sets of sample data, including steps for calculating the mean and standard deviation. This problem covers key statistical concepts, such as measures of variability, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation