If mode of any series is 9 and median is 7 then mean of that series will be

Options

A. `-6`
B. `6`
C. `-5//3`
D. `5//3`

Answer

To find the mean of a series when the mode is 9 and the median is 7, we can use the relationship between these three measures of central tendency.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between mode, median, and mean can be expressed as:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]

2. **Substitute the Known Values**:
We know that:
- Mode = 9
- Median = 7

Plugging these values into the equation gives us:
\[ 9 = 3 \times 7 - 2 \times \text{Mean} \]

3. **Calculate the Right Side**:
Calculate \(3 \times 7\):
\[ 3 \times 7 = 21 \]
So, the equation now looks like:
\[ 9 = 21 - 2 \times \text{Mean} \]

4. **Rearrange the Equation**:
To isolate the mean, rearrange the equation:
\[ 2 \times \text{Mean} = 21 - 9 \]

5. **Simplify the Right Side**:
Calculate \(21 - 9\):
\[ 21 - 9 = 12 \]
So, now we have:
\[ 2 \times \text{Mean} = 12 \]

6. **Solve for the Mean**:
Divide both sides by 2 to find the mean:
\[ \text{Mean} = \frac{12}{2} = 6 \]

Thus, the mean of the series is **6**.