The mean of range, mode and median of the data 4, 3, 2, 2, 7, 2, 2, 0, 3, 4, 4 is

Options

A. 4
B. 3
C. 5
D. 2

Answer

To find the mean of the range, mode, and median of the given data set \(4, 3, 2, 2, 7, 2, 2, 0, 3, 4, 4\), we will follow these steps:

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

**Data in ascending order:**
\[0, 2, 2, 2, 2, 3, 3, 4, 4, 4, 7\]

### Step 2: Calculate the Median
The median is the middle value of a data set. Since there are 11 numbers (which is odd), the median will be the value at position \((n + 1) / 2\), where \(n\) is the number of observations.

**Calculation:**
\[n = 11\]
Median position = \((11 + 1) / 2 = 12 / 2 = 6\] The 6th value in the ordered list is \(3\).
**Median = 3**

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

**Counting occurrences:**
- \(0\) appears \(1\) time
- \(2\) appears \(4\) times
- \(3\) appears \(2\) times
- \(4\) appears \(3\) times
- \(7\) appears \(1\) time

The most frequent value is \(2\).
**Mode = 2**

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

**Calculation:**
- Highest value = \(7\)
- Lowest value = \(0\)

**Range = Highest value - Lowest value = 7 - 0 = 7**

### Step 5: Calculate the Mean of Range, Mode, and Median
Now, we need to find the mean of the three values we calculated: median, mode, and range.

**Values:**
- Median = \(3\)
- Mode = \(2\)
- Range = \(7\)

**Calculation of mean:**
Mean = \(\frac{\text{Median} + \text{Mode} + \text{Range}}{3} = \frac{3 + 2 + 7}{3} = \frac{12}{3} = 4\)

### Final Answer
**The mean of the range, mode, and median is \(4\).**

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