What is the mean of the median, mode and range for the data given below ?
11, 25, 0, 8, 25, 30, 44, 50, 30, 18, 20, 17, 11, 9, 24, 25, 29

Question

Accepted Answer

To determine the mean of the median, mode, and range for the given data set, we need to calculate each of these statistical measures and then find their average.

**Data Set:** 11, 25, 0, 8, 25, 30, 44, 50, 30, 18, 20, 17, 11, 9, 24, 25, 29

1. **Median:**
   - First, arrange the data in ascending order: 0, 8, 9, 11, 11, 17, 18, 20, 24, 25, 25, 25, 29, 30, 30, 44, 50
   - The median is the middle value. Since there are 17 numbers, the median is the 9th value: 24

2. **Mode:**
   - The mode is the number that appears most frequently. In this data set, 25 appears three times, more than any other number.
   - Therefore, the mode is 25.

3. **Range:**
   - The range is the difference between the maximum and minimum values.
   - Maximum value = 50, Minimum value = 0
   - Range = 50 - 0 = 50

4. **Mean of the Median, Mode, and Range:**
   - Mean = (Median + Mode + Range) / 3
   - Mean = (24 + 25 + 50) / 3 = 99 / 3 = 33

Therefore, the mean of the median, mode, and range is 33, which corresponds to Option 3.

**Explanation of Incorrect Options:**

- **Option 1 (31):** This option is incorrect because the calculated mean of 33 does not match 31. The arithmetic operations and the values of median, mode, and range do not support this option.

- **Option 2 (32):** This option is incorrect because the mean of 33 is not equal to 32. The calculations clearly show that the mean is 33, not 32.

- **Option 4 (34):** This option is incorrect because the mean of 33 is less than 34. The calculated mean from the given data set does not support this option.

In conclusion, the correct answer is Option 3, as the mean of the median, mode, and range is indeed 33.