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Question

A bar graph is titled 'Number of States Visited by Students.' The x-axis is labeled 'Number of States Visited' and ranges from 0 to 5 by unit increments. The y-axis is labeled 'Number of Students' and ranges from 0 to 6 in increments of 2.

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

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

To find the balancing point (mean) of the dataset represented in the bar graph, you would need to calculate the weighted average based on the number of states visited and the number of students.

Here’s a step-by-step method to find it:

1. Identify the data from the graph. For example, if the graph shows that:

   • 0 states were visited by 2 students
   • 1 state was visited by 3 students
   • 2 states were visited by 4 students
   • 3 states were visited by 5 students
   • 4 states were visited by 6 students
   • 5 states were visited by 1 student

2. Create a table of "Number of States Visited" (X) and "Number of Students" (f):

   • (0, 2)
   • (1, 3)
   • (2, 4)
   • (3, 5)
   • (4, 6)
   • (5, 1)

3. Calculate the total number of students (N): N = 2 + 3 + 4 + 5 + 6 + 1 = 21

4. Calculate the sum of products of the number of states visited times the number of students for each category (ΣXf): ΣXf = (02) + (13) + (24) + (35) + (46) + (51) = 0 + 3 + 8 + 15 + 24 + 5 = 55

5. The mean (M) or balancing point is given by: M = ΣX*f / N = 55 / 21 ≈ 2.62 (rounded to two decimal places)

Thus, the balancing point of the dataset is approximately 2.62.