Question

Team A: 1,2,3,3,3,4,5
Team B : 2,2,2,3,3,4,4,4
What is the difference of the means and the quotient of the mean deviation

Answer 1

To find the difference of the means and the quotient of the mean deviations for Team A and Team B, we will calculate the mean and mean deviation for both teams step-by-step.

### Step 1: Calculate the Mean for Each Team

**Team A:**
Data: 1, 2, 3, 3, 3, 4, 5
- Mean (μA) = (1 + 2 + 3 + 3 + 3 + 4 + 5) / 7
- Mean (μA) = 21 / 7
- Mean (μA) = 3

**Team B:**
Data: 2, 2, 2, 3, 3, 4, 4, 4
- Mean (μB) = (2 + 2 + 2 + 3 + 3 + 4 + 4 + 4) / 8
- Mean (μB) = 24 / 8
- Mean (μB) = 3

### Step 2: Calculate the Mean Deviation for Each Team

Mean Deviation (MD) is calculated as the average of the absolute deviations from the mean.

**Team A Mean Deviation:**
- Absolute deviations from the mean (3):
- |1 - 3| = 2
- |2 - 3| = 1
- |3 - 3| = 0
- |3 - 3| = 0
- |3 - 3| = 0
- |4 - 3| = 1
- |5 - 3| = 2

- Mean Deviation (MD_A) = (2 + 1 + 0 + 0 + 0 + 1 + 2) / 7
- Mean Deviation (MD_A) = 6 / 7
- Mean Deviation (MD_A) ≈ 0.857

**Team B Mean Deviation:**
- Absolute deviations from the mean (3):
- |2 - 3| = 1
- |2 - 3| = 1
- |2 - 3| = 1
- |3 - 3| = 0
- |3 - 3| = 0
- |4 - 3| = 1
- |4 - 3| = 1
- |4 - 3| = 1

- Mean Deviation (MD_B) = (1 + 1 + 1 + 0 + 0 + 1 + 1 + 1) / 8
- Mean Deviation (MD_B) = 5 / 8
- Mean Deviation (MD_B) = 0.625

### Step 3: Calculate the Difference of the Means and the Quotient of the Mean Deviations

**Difference of the Means:**
- Difference = μA - μB
- Difference = 3 - 3 = 0

**Quotient of the Mean Deviations:**
- Quotient = MD_A / MD_B
- Quotient = (6 / 7) / (5 / 8) = (6/7) * (8/5) = (48 / 35)

### Final Results
1. Difference of the Means: **0**
2. Quotient of the Mean Deviations: **\(\frac{48}{35}\) or approximately 1.37**