https://file.aiquickdraw.com/mathbot/file/1726744406697rhikf5ct.jpg

Here are the statistics for Michael's grades in the first and second quarters:

### First Quarter:
1. **Range**: 17
2. **Mean Absolute Deviation (MAD)**: 4.22
3. **Variance**: 26.98
4. **Standard Deviation**: 5.19

### Second Quarter:
1. **Range**: 4
2. **Mean Absolute Deviation (MAD)**: 0.88
3. **Variance**: 1.23
4. **Standard Deviation**: 1.11

### Coefficient of Variation:
- **First Quarter**: 5.80%
- **Second Quarter**: 1.24%

#### Comparison:
- The first quarter has a wider spread of grades (larger range, variance, and standard deviation) than the second quarter. The coefficient of variation is also higher in the first quarter, indicating greater variability in performance. The second quarter shows more consistency with less variation in grades.

Would you like further clarification on any of the terms or details?

Here are 5 related questions to deepen your understanding:
1. How is the coefficient of variation useful in comparing two data sets?
2. Why is the standard deviation larger in the first quarter compared to the second?
3. How does the mean absolute deviation (MAD) differ from standard deviation?
4. What other statistical measures can be used to analyze data spread?
5. How could Michael use these statistics to improve his future grades?

**Tip**: The lower the coefficient of variation, the more consistent the data set is relative to the mean.

Michael is a hardworking student. Compute for the range, MAD, variance, and standard deviation of each set of grades in the first and second quarter. Calculate the coefficient of variation of Michael’s grades for every quarter. Compare his performance for the 2 quarters.

Learn how to calculate the range, MAD, variance, and standard deviation of Michael's grades for two quarters. Compare the coefficient of variation for each quarter and analyze the consistency of his performance.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation