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

Options

A. 31
B. 32
C. 33
D. 34

Answer

To find the mean of the median, mode, and range for the given data set, we will follow these steps:

### Step 1: Organize the Data
First, we need to arrange the data in ascending order.

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

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

### Step 2: Calculate the Median
The median is the middle value of the data set. Since there are 17 numbers (which is odd), the median will be the value at position (n + 1) / 2, where n is the total number of data points.

**Calculation:**
- Total numbers (n) = 17
- Median position = (17 + 1) / 2 = 18 / 2 = 9

The 9th term in the ordered list is 24.

**Median = 24**

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

**Data Analysis:**
- The number 25 appears 3 times.
- All other numbers appear less frequently.

**Mode = 25**

### Step 4: Calculate the Range
The range is the difference between the highest and lowest values in the data set.

**Calculation:**
- Highest value = 50
- Lowest value = 0

**Range = Highest - Lowest = 50 - 0 = 50**

### Step 5: Calculate the Mean of Median, Mode, and Range
Now we will find the mean of the median, mode, and range.

**Calculation:**
- Median = 24
- Mode = 25
- Range = 50

**Mean = (Median + Mode + Range) / 3 = (24 + 25 + 50) / 3 = 99 / 3 = 33**

### Final Answer
**The mean of the median, mode, and range is 33.**

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