Question

Pamela has the following data:

1415q1614161514
If the mean is 15, which number could q be

Answer 1

To find the value of \( q \) such that the mean of the dataset is 15, we first need to determine the total number of data points and the sum of the data points in the dataset.

The dataset reads: \( 1415, q, 1614, 1615, 14 \).

Let's break it down:

1. Count the total number of numbers:
- There are 5 numbers: \( 1415, q, 1614, 1615, 14 \).

2. The mean is calculated as follows:

\[
\text{Mean} = \frac{\text{Sum of data points}}{\text{Number of data points}}
\]

Given that the mean is 15:

\[
15 = \frac{1415 + q + 1614 + 1615 + 14}{5}
\]

3. Calculate the sum of the known data points:

\[
1415 + 1614 + 1615 + 14 = 4158
\]

4. Substitute this sum into the equation:

\[
15 = \frac{4158 + q}{5}
\]

5. Multiply both sides by 5 to eliminate the fraction:

\[
75 = 4158 + q
\]

6. Solve for \( q \):

\[
q = 75 - 4158 = -4083
\]

Thus, \( q \) could be \( -4083 \).