The mode of a distribution is 24 and the mean is 60. Whatis its median?

Options

A. 48
B. 50
C. 45
D. 51

Answer

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

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

Given:
- Mode = 24
- Mean = 60

We need to find the Median.

### Step 1: Substitute the known values into the formula.

We start by substituting the values of the mean and mode into the formula:

\[ 60 - 24 = 3 \times (60 - \text{Median}) \]

### Step 2: Simplify the left side of the equation.

Calculating the left side:

\[ 60 - 24 = 36 \]

So now we have:

\[ 36 = 3 \times (60 - \text{Median}) \]

### Step 3: Divide both sides by 3.

To isolate the term involving the median, we divide both sides of the equation by 3:

\[ \frac{36}{3} = 60 - \text{Median} \]

This simplifies to:

\[ 12 = 60 - \text{Median} \]

### Step 4: Rearrange the equation to solve for the Median.

Now, we can rearrange the equation to solve for the Median:

\[ \text{Median} = 60 - 12 \]

### Step 5: Calculate the Median.

Now, we perform the final calculation:

\[ \text{Median} = 48 \]

Thus, the median of the distribution is **48**.

### Summary of Steps:
1. Substitute known values into the formula.
2. Simplify the left side of the equation.
3. Divide both sides by 3.
4. Rearrange the equation to solve for the Median.
5. Calculate the Median.