Use the mean to find the balancing point of the given data set in the graph number of states visited one two three four five number of students one state six students two states three students three states one student four states three students five states six students

Answer 1

To find the mean (or balancing point) of the given data set, we need to determine the total number of students and the total number of states visited. Let's summarize the data first:

1. One state: 6 students
2. Two states: 3 students
3. Three states: 3 students
4. Four states: 1 student
5. Five states: 3 students
6. Six states: 6 students

Now, we can calculate the total number of students and the total number of states visited:

1. The total number of students can be calculated by adding the number of students: \[ 6 + 3 + 3 + 1 + 3 + 6 = 22 \text{ students} \]

2. To find the total number of states visited, each category needs to be multiplied by the number of students in that category, then summed: \[ (1 \times 6) + (2 \times 3) + (3 \times 3) + (4 \times 1) + (5 \times 3) + (6 \times 6) \] \[ = 6 + 6 + 9 + 4 + 15 + 36 = 76 \text{ total states visited} \]

Now, we can compute the mean (balancing point) using the formula: \[ \text{Mean} = \frac{\text{Total states visited}}{\text{Total students}} = \frac{76}{22} \]

Dividing 76 by 22 gives: \[ \text{Mean} \approx 3.45 \]

Therefore, the balancing point of the given data set is approximately 3.45 states.