The heights (in cm) of the volley-ball players from team A and term B were recorded as :
Team A : 180, 178, 176, 181, 190, 175, 187
Team B : 174, 175, 190, 179, 178, 185, 177
Which team had the greater average height ?
Find the median of team A and team B.

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the Mean Height of Team A
1. **List the heights of Team A**: 180, 178, 176, 181, 190, 175, 187
2. **Sum the heights**:
\[ 180 + 178 + 176 + 181 + 190 + 175 + 187 = 1267 \]
3. **Count the number of players**: There are 7 players in Team A.
4. **Calculate the mean**:
\[ \text{Mean} = \frac{\text{Sum of heights}}{\text{Number of players}} = \frac{1267}{7} = 181 \text{ cm} \]

### Step 2: Calculate the Mean Height of Team B
1. **List the heights of Team B**: 174, 175, 190, 179, 178, 185, 177
2. **Sum the heights**:
\[ 174 + 175 + 190 + 179 + 178 + 185 + 177 = 1258 \]
3. **Count the number of players**: There are 7 players in Team B.
4. **Calculate the mean**:
\[ \text{Mean} = \frac{\text{Sum of heights}}{\text{Number of players}} = \frac{1258}{7} \approx 179.71 \text{ cm} \]

### Step 3: Compare the Mean Heights
- Team A Mean Height: 181 cm
- Team B Mean Height: 179.71 cm
- **Conclusion**: Team A has a greater average height.

### Step 4: Find the Median Height of Team A
1. **Arrange the heights of Team A in ascending order**: 175, 176, 178, 180, 181, 187, 190
2. **Find the median**:
- Total number of observations (N) = 7 (odd)
- Median position = \(\frac{N + 1}{2} = \frac{7 + 1}{2} = 4\)
- The 4th observation in the ordered list is 180 cm.

### Step 5: Find the Median Height of Team B
1. **Arrange the heights of Team B in ascending order**: 174, 175, 177, 178, 179, 185, 190
2. **Find the median**:
- Total number of observations (N) = 7 (odd)
- Median position = \(\frac{N + 1}{2} = \frac{7 + 1}{2} = 4\)
- The 4th observation in the ordered list is 178 cm.

### Final Results
- **Mean Height**: Team A = 181 cm, Team B = 179.71 cm
- **Median Height**: Team A = 180 cm, Team B = 178 cm