Which one is correct for the following data?
`-2, 2, 1, 0, 5, 4, 5, 7, 5, 11, 12

Options

A. Mean = Median = Mode
B. Median = Mode
C. Mean = 5
D. Mean = Mode

Answer

To solve the problem, we need to find the mean, median, and mode of the given data set: `-2, 2, 1, 0, 5, 4, 5, 7, 5, 11, 12`.

### Step-by-Step Solution:

1. **Arrange the Data in Ascending Order:**
- The first step is to sort the data in ascending order.
- Sorted Data: `-2, 0, 1, 2, 4, 5, 5, 5, 7, 11, 12`.

2. **Calculate the Median:**
- The median is the middle value of a data set when it is ordered.
- Count the number of terms (N): There are 11 terms.
- Since N is odd, the median is the value at the (N + 1) / 2 position.
- Position: (11 + 1) / 2 = 12 / 2 = 6.
- The 6th term in the sorted data is 5.
- **Median = 5**.

3. **Calculate the Mean:**
- The mean is calculated by summing all the terms and dividing by the number of terms.
- Sum of terms: -2 + 0 + 1 + 2 + 4 + 5 + 5 + 5 + 7 + 11 + 12 = 50.
- Number of terms (N) = 11.
- Mean = Sum of terms / N = 50 / 11 ≈ 4.54.
- **Mean ≈ 4.54**.

4. **Calculate the Mode:**
- The mode is the value that appears most frequently in the data set.
- In the sorted data, the number 5 appears 3 times, while all other numbers appear less frequently.
- **Mode = 5**.

5. **Compare Mean, Median, and Mode:**
- We have calculated:
- Mean ≈ 4.54
- Median = 5
- Mode = 5
- The median and mode are equal (both are 5), while the mean is approximately 4.54.

### Conclusion:
The correct statement regarding the data is that the **median is equal to the mode**.