Given the set of data 1,1,2,2,2,3,3,4, which one of the following statements is true?

Options

A. mean `le`median`le`mode
B. median`le`mean`le`mode
C. median`le`mode`le`mean
D. mode`le`mean`le`median

Explanation

To solve the problem, we need to find the mean, median, and mode of the given data set: 1, 1, 2, 2, 2, 3, 3, 4.

### Step 1: Calculate the Mean
The mean is calculated by taking the sum of all the values and dividing it by the number of values.

1. **Sum of the data**:
- \(1 + 1 + 2 + 2 + 2 + 3 + 3 + 4 = 18\)

2. **Number of values**:
- There are 8 values in total.

3. **Mean calculation**:
- \(\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{18}{8} = 2.25\)

### Step 2: Calculate the Median
The median is the middle value of the ordered data set.

1. **Order the data**:
- The data is already ordered: 1, 1, 2, 2, 2, 3, 3, 4.

2. **Find the middle values**:
- Since there are 8 values (an even number), the median will be the average of the 4th and 5th values.
- The 4th value is 2 and the 5th value is also 2.

3. **Median calculation**:
- \(\text{Median} = \frac{2 + 2}{2} = 2\)

### Step 3: Calculate the Mode
The mode is the value that appears most frequently in the data set.

1. **Count the frequency of each value**:
- 1 appears 2 times
- 2 appears 3 times
- 3 appears 2 times
- 4 appears 1 time

2. **Identify the mode**:
- The value that appears most frequently is 2 (it appears 3 times).

### Summary of Results
- Mean: 2.25
- Median: 2
- Mode: 2

### Conclusion
Now we can analyze the relationships between the mean, median, and mode:
- Mean (2.25) > Median (2)
- Mean (2.25) > Mode (2)

Thus, the statement that is true is that the mean is greater than both the median and the mode.

### Final Answer
The correct statement is: The mean is greater than both the median and the mode.