The median and mode of a frequency distribution are 26 and 29 respectively. Then , the mean is

Options

A. 27.5
B. 24.5
C. 28.4
D. 25.8

Explanation

To find the mean of a frequency distribution when the median and mode are given, we can use the relationship between these three measures of central tendency. The formula that relates mode, median, and mean is:

\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]

Given:
- Median = 26
- Mode = 29

We need to find the mean. Let's denote the mean as \( \text{Mean} \).

### Step 1: Substitute the values into the formula
Using the formula, we can rearrange it to find the mean:

\[ 29 = 3 \times 26 - 2 \times \text{Mean} \]

### Step 2: Calculate \( 3 \times 26 \)
Now, calculate \( 3 \times 26 \):

\[ 3 \times 26 = 78 \]

### Step 3: Substitute back into the equation
Now substitute this value back into the equation:

\[ 29 = 78 - 2 \times \text{Mean} \]

### Step 4: Rearrange the equation to isolate \( 2 \times \text{Mean} \)
Rearranging gives us:

\[ 2 \times \text{Mean} = 78 - 29 \]

### Step 5: Calculate \( 78 - 29 \)
Now calculate \( 78 - 29 \):

\[ 78 - 29 = 49 \]

### Step 6: Solve for the mean
Now we have:

\[ 2 \times \text{Mean} = 49 \]

To find the mean, divide both sides by 2:

\[ \text{Mean} = \frac{49}{2} \]

### Step 7: Calculate \( \frac{49}{2} \)
Calculating \( \frac{49}{2} \):

\[ \text{Mean} = 24.5 \]

### Conclusion
Thus, the mean of the frequency distribution is **24.5**.

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