Question

Use the mean to find the balancing point of the given dataset in the graph.


A bar graph displays the number of students who visited a certain number of states.

The x-axis is labeled "Number of States Visited" and shows values from 1 to 5. The y-axis is labeled "Number of Students" and shows values from 0 to 6.

The bars represent the frequency of students who visited each number of states.

* One student visited 1 state. * Three students visited 2 states. * One student visited 3 states. * Three students visited 4 states. * Six students visited 5 states.


(1 point)
The balancing point of the dataset is
.

Answer 1

To find the balancing point (mean) of the dataset, we first need to calculate the total number of students and the total "value" contributed by the number of states visited.

The data provided is:
- 1 student visited 1 state
- 3 students visited 2 states
- 1 student visited 3 states
- 3 students visited 4 states
- 6 students visited 5 states

Now, let's calculate the total number of students:

\[
\text{Total students} = 1 + 3 + 1 + 3 + 6 = 14
\]

Next, we need to calculate the total value contributed by each group of students based on the number of states they visited. We multiply the number of students by the corresponding number of states visited:

\[
\text{Total value} = (1 \times 1) + (3 \times 2) + (1 \times 3) + (3 \times 4) + (6 \times 5)
\]

Calculating each term:
- \(1 \times 1 = 1\)
- \(3 \times 2 = 6\)
- \(1 \times 3 = 3\)
- \(3 \times 4 = 12\)
- \(6 \times 5 = 30\)

Now sum these values:

\[
\text{Total value} = 1 + 6 + 3 + 12 + 30 = 52
\]

Now we can find the mean (balancing point) by dividing the total value by the total number of students:

\[
\text{Mean} = \frac{\text{Total value}}{\text{Total students}} = \frac{52}{14} \approx 3.71
\]

Thus, the balancing point of the dataset is approximately **3.71**.