Question

Pamela has the following data:

14 15 q 16 14 16 15 14
If the mean is 15, which number could q be

Answer 1

To find the value of \( q \) such that the mean of the numbers is 15, we first calculate the total number of values and then set up the equation for the mean.

The numbers include: \( 14, 15, q, 16, 14, 16, 15, 14 \).

There are 8 values in total. The formula for the mean is:

\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = 15
\]

So, we set up the equation:

\[
\frac{14 + 15 + q + 16 + 14 + 16 + 15 + 14}{8} = 15
\]

Calculating the sum of the numbers without \( q \):

\[
14 + 15 + 16 + 14 + 16 + 15 + 14 = 14 + 14 + 14 + 15 + 15 + 16 + 16 = 14 \times 3 + 15 \times 2 + 16 \times 2
\]

Calculating each part:

- \( 14 \times 3 = 42 \)
- \( 15 \times 2 = 30 \)
- \( 16 \times 2 = 32 \)

Now, adding those results together:

\[
42 + 30 + 32 = 104
\]

Thus, the equation becomes:

\[
\frac{104 + q}{8} = 15
\]

To eliminate the fraction, we multiply both sides by 8:

\[
104 + q = 120
\]

Now, solving for \( q \):

\[
q = 120 - 104 = 16
\]

Thus, the value of \( q \) that makes the mean 15 is \( \boxed{16} \).