Question

A group of 17 students participated in a quiz competition. Their scores are shown below:

Score 0–4 5–9 10–14 15–19 20–24
Number of students 4 5 2 3 3
Part A: Would a dot plot, a histogram, or a box plot best represent the data shown above. Explain your answer. (4 points)

Part B: Provide a step-by-step description of how you would create the graph named in Part A. (6 points)

Answer 1

Part A is a histogram.

Part B draw a histogram

Step-by-step explanation:

This is because a dot plot and a box plot are too specific for how the data was given. We don't know the exact number for each student.

Part B The x axis would be labeled by the groups, 0-4, 5-9, 10-14, 15-19, 20-24. The y axis would be labeled number of students. Then you could color in the area matching the correct number of students for each category.

Answer 2

Part A

Answer: Histogram

Step-by-step explanation:

A histogram is best because it helps show how the scores breakdown for the various bins or intervals or classes. It's effectively a visual summary of a grouped frequency table.

A dot plot would not work because we don't know the specific scores, but rather just the general region of where they fall.

A box plot doesn't work well either because we lose information on how the distribution is broken down. Sure we get the five number summary out of it, but we don't see how the bins are set up.

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Part B

We have the categories or bins of 0-4, 5-9, 10-14, 15-19, 20-24. Each bin will correspond to a bar that tells us how frequently the values show up. It tells us how frequent or how many scores we got in that sub-interval.

• The bin 0-4 has a bar that is 4 units high which means we got 4 scores that are between 0 and 4
• The bin 5-9 has a bar that is 5 units high, so we have 5 scores between 5 and 9.
• The bin 10-14 has a bar that is 2 units high since we have 2 scores in this region.

And so on. This all leads to the histogram shown below.