The mean of 7 numbers is 14. Each number is multiplied by 3 and then 2 is subtracted from every result. What is the new mean?

**Formula**: $x$̄ = (sum of observations) / (number of observations) = Σ$x/n$.

**Example**: Marks of 5 students: 7, 8, 6, 9, 10.
Sum = 40, $n=5$. Mean = 40/5 = 8.

**For a frequency distribution**:
$x$̄ = Σ$(f$ᵢ$x$ᵢ) / Σ$f$ᵢ
Multiply each value by its frequency, sum, and divide by total frequency.

Example: marks 5, 7, 9 with frequencies 2, 3, 5.
Σ$fx=5$·2 + 7·3 + 9·5 = 10 + 21 + 45 = 76.
Σ$f=10$. Mean = 76 / 10 = 7.6.