💣 Q :144 Prep 1 Question Bank T1

If the arithmetic mean of the numbers \(16, n + 3, 14, 2n - 2\) is \(15.25\), find the median of these numbers.

Solution:

1. Calculate the sum of numbers using the mean:

\[ \frac{16 + (n + 3) + 14 + (2n - 2)}{4} = 15.25 \]

2. Simplify the equation:

\[ 16 + n + 3 + 14 + 2n - 2 = 61 \] \[ 3n + 31 = 61 \]

3. Solve for \(n\):

\[ 3n = 30 \implies n = 10 \]

4. Find all four numbers:

\[ 16, \quad n + 3 = 13, \quad 14, \quad 2n - 2 = 18 \]

5. Arrange in order and find median:

\[ \text{Ordered numbers: } 13, 14, 16, 18 \] \[ \text{Median} = \frac{14 + 16}{2} = \boxed{15} \]

b) Multiple choice: What is the value of \(n\) in this problem?

MR/Nasef.N