If mode of a grouped data is 10 and mean is 4, then median will be

Options

A. 1
B. 4
C. 6
D. 8

Answer

To find the median of the grouped data when the mode is 10 and the mean is 4, we can use the relationship between mean, median, and mode. Here’s a step-by-step solution:

### Step 1: Write down the given values
- Mean (M) = 4
- Mode (Mo) = 10

### Step 2: Use the relationship between mean, median, and mode
The relationship is given by the formula:
\[ Mo = 3 \times \text{Median} - 2 \times \text{Mean} \]

### Step 3: Substitute the known values into the formula
Substituting the known values into the formula:
\[ 10 = 3 \times \text{Median} - 2 \times 4 \]

### Step 4: Simplify the equation
Calculate \(2 \times 4\):
\[ 2 \times 4 = 8 \]
Now substitute this back into the equation:
\[ 10 = 3 \times \text{Median} - 8 \]

### Step 5: Rearrange the equation to isolate the median
Add 8 to both sides:
\[ 10 + 8 = 3 \times \text{Median} \]
\[ 18 = 3 \times \text{Median} \]

### Step 6: Solve for the median
Divide both sides by 3:
\[ \text{Median} = \frac{18}{3} \]
\[ \text{Median} = 6 \]

### Conclusion
Thus, the median of the grouped data is **6**.

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