The car chart shows, on the x axis of the line chart is the number of states visited(one to five), on the y-axis is the number of students(, zero to six, 1,3,and 5 are missing) number one goes up to six, number two goes up to three, number three goes up to one, number four goes up to three,number 5 goes up to six,Use the mean to find the balancing point of the given dataset in the graph.

Question

The car chart  shows, on the x axis of the line chart is the number of states visited(one to five), on the y-axis is the number of students(, zero to six, 1,3,and 5 are missing)  number one goes up to six, number two goes up to three, number three goes up to one, number four goes up to three,number 5 goes up to six,Use the mean to find the balancing point of the given dataset in the graph.

GPT-4o mini · Answer

To find the mean (or balancing point) of the dataset based on the provided information about the number of states visited and the number of students, we'll first summarize the data you've given:

1 state visited: 6 students
2 states visited: 3 students
3 states visited: 1 student
4 states visited: 3 students
5 states visited: 6 students

Step 1: Calculate the weighted sum

For each category, we multiply the number of states visited (x value) by the number of students (y value).

For 1 state: \( 1 \times 6 = 6 \)
For 2 states: \( 2 \times 3 = 6 \)
For 3 states: \( 3 \times 1 = 3 \)
For 4 states: \( 4 \times 3 = 12 \)
For 5 states: \( 5 \times 6 = 30 \)

Step 2: Sum the weighted values

Now we sum these products:

\[ 6 + 6 + 3 + 12 + 30 = 57 \]

Step 3: Sum the number of students

Next, we sum the total number of students:

\[ 6 + 3 + 1 + 3 + 6 = 19 \]

Step 4: Calculate the mean

Now, we can calculate the mean by dividing the weighted sum by the total number of students:

\[ \text{Mean} = \frac{57}{19} \approx 3 \]

Conclusion

The balancing point (mean number of states visited) for the given dataset is approximately 3.