Which of the following is correct for data -1, 0, 1,2,3,5,5,6,8,10,11

Options

A. mean = mode = median
B. mean = 5
C. mean = mode
D. mode = median

Answer

To solve the problem, we need to find the mean, median, and mode of the given data set: -1, 0, 1, 2, 3, 5, 5, 6, 8, 10, 11.

### Step-by-Step Solution:

**Step 1: Calculate the Mean**
- The mean is calculated by summing all the values and dividing by the number of values.
- The formula for mean is:
\[ \text{Mean} = \frac{\sum X_i}{n} \]
where \( \sum X_i \) is the sum of all data points and \( n \) is the number of data points.

- First, we sum the data:
\[ -1 + 0 + 1 + 2 + 3 + 5 + 5 + 6 + 8 + 10 + 11 = 50 \]

- Next, we count the number of data points:
\[ n = 11 \]

- Now, we can calculate the mean:
\[ \text{Mean} = \frac{50}{11} \approx 4.545 \]

**Step 2: Calculate the Median**
- The median is the middle value when the data is arranged in ascending order.
- Since there are 11 data points (an odd number), the median is the value at position \( \frac{n+1}{2} \).

- The position of the median is:
\[ \frac{11 + 1}{2} = 6 \]

- The 6th value in the ordered data set (-1, 0, 1, 2, 3, 5, 5, 6, 8, 10, 11) is 5.

- Therefore, the median is:
\[ \text{Median} = 5 \]

**Step 3: Calculate the Mode**
- The mode is the value that appears most frequently in the data set.
- In this data set, the number 5 appears twice, while all other numbers appear only once.

- Therefore, the mode is:
\[ \text{Mode} = 5 \]

### Summary of Results:
- Mean: \( \approx 4.545 \)
- Median: \( 5 \)
- Mode: \( 5 \)

### Conclusion:
From our calculations, we find that:
- The mean is approximately 4.545.
- The median is 5.
- The mode is 5.

Thus, the correct statement regarding the data is that the mode is equal to the median.