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

Question

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

Accepted Answer

To determine why Option 2 is the correct answer, we need to calculate the mean, median, and mode of the given data set: -2, 2, 1, 0, 5, 4, 5, 7, 5, 11, 12.

1. **Calculating the Mean:**
   The mean is the average of all the numbers. To find it, we sum all the numbers and divide by the count of numbers.
   $$
   \text{Mean} = \frac{-2 + 2 + 1 + 0 + 5 + 4 + 5 + 7 + 5 + 11 + 12}{11} = \frac{50}{11} \approx 4.545
   $$

2. **Calculating the Median:**
   The median is the middle value when the numbers are arranged in order. First, we arrange the data:
   -2, 0, 1, 2, 4, 5, 5, 5, 7, 11, 12
   Since there are 11 numbers, the median is the 6th number:
   $$
   \text{Median} = 5
   $$

3. **Calculating the Mode:**
   The mode is the number that appears most frequently. In this data set, the number 5 appears three times, more than any other number.
   $$
   \text{Mode} = 5
   $$

**Explanation for Option 2: Median = Mode**

- The median of the data set is 5.
- The mode of the data set is also 5.
- Therefore, the median equals the mode, which supports Option 2 as the correct answer.

**Explanation for why other options are incorrect:**

1. **Option 1: Mean = Median = Mode**
   - The mean is approximately 4.545, while the median and mode are both 5. Since the mean is not equal to the median or the mode, this option is incorrect.

2. **Option 3: Mean = 5**
   - As calculated, the mean is approximately 4.545, not 5. Therefore, this option is incorrect.

3. **Option 4: Mean = Mode**
   - The mean is approximately 4.545, while the mode is 5. Since these values are not equal, this option is incorrect.

In conclusion, Option 2 is correct because the median and mode of the data set are both 5, fulfilling the condition specified in the option.