Question

Find the mean of numbers randomly selected from 1 to 15.

Hint:

To find the mean of an arithmetic series, use the formula \( \frac{n}{2} \times (a + l) \), where \( n \) is the number of terms, \( a \) is the first term, and \( l \) is the last term.

Answer 1

The mean of the numbers from 1 to 15 is given by the formula: \[ \text{Mean} = \frac{\text{Sum of all numbers}}{\text{Number of numbers}} \] The sum of the numbers from 1 to 15 is the sum of an arithmetic series: \[ S = \frac{n}{2} \left( a + l \right) \] where \( n = 15 \), \( a = 1 \), and \( l = 15 \). So, \[ S = \frac{15}{2} \left( 1 + 15 \right) = \frac{15}{2} \times 16 = 120 \] The number of numbers is 15. Therefore, the mean is: \[ \text{Mean} = \frac{120}{15} = 8 \] Thus, the mean is: \[ \boxed{8} \]