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Use the image to answer the question.

Bar graph
Y axis frequency: 0 1 2 3 4 5
X axis number of activities: 0 1 2 3 4 5
BAR DATA: 1 2 5 2 1

Which of the following options is true about the relationship between the mean and median of the data in the graph?

Option #1: The mean is greater than the median.

Option #2: The mean is less than the median.

Option #3: The mean is equal to the median.

(1 point)
Option # is the true statement.

1 answer

To determine the relationship between the mean and median based on the bar graph data provided, we first need to calculate both the mean and median.

From the bar graph, we have the frequency of activities as follows:

  • 0 activities: 1 time
  • 1 activity: 2 times
  • 2 activities: 5 times
  • 3 activities: 2 times
  • 4 activities: 1 time

Now organizing this information, the data points can be listed out based on the frequency:

  • 0, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4

  • Total data points: 11

Step 1: Calculate the mean Mean = (Sum of all data points) / (Number of data points)

Sum of the data points: = (0 * 1) + (1 * 2) + (2 * 5) + (3 * 2) + (4 * 1) = 0 + 2 + 10 + 6 + 4 = 22

Mean = 22 / 11 = 2

Step 2: Calculate the median The median is the middle value in a sorted list. For 11 data points, the median is the 6th value.

Sorted data: 0, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4

The 6th value is 2, so the median is 2.

Final Comparison:

  • Mean = 2
  • Median = 2

Thus, the mean is equal to the median.

The true statement is: Option #3: The mean is equal to the median.