Question

The scores for today’s math quiz are 75, 95, 60, 75, 95, and 80. Explain the steps needed to create a histogram for the data.

Answer 1

Steps to make a histogram for the scores 75, 95, 60, 75, 95, 80:

1. Look at the data
- Minimum = 60, maximum = 95, range = 35.

2. Choose the number of bins (class intervals)
- For a small set 4 bins works well. (You could also choose 5–6 bins or one bin per unique score.)

3. Compute a convenient bin width
- width ≈ range / number of bins = 35 / 4 ≈ 8.75 → use a round width of 10 for neat intervals.

4. Set the class intervals
- Using width 10: 60–69, 70–79, 80–89, 90–99.

5. Count frequencies for each bin
- 60–69: 60 → 1
- 70–79: 75, 75 → 2
- 80–89: 80 → 1
- 90–99: 95, 95 → 2

Frequency table:
- 60–69 : 1
- 70–79 : 2
- 80–89 : 1
- 90–99 : 2

6. Draw the histogram
- Horizontal axis: the score intervals (60–69, 70–79, 80–89, 90–99).
- Vertical axis: frequency (0,1,2,...).
- For each interval draw a bar whose height equals its frequency. Make the bars touch (no gaps) because histogram bins are continuous intervals.

7. Add labels and title
- Title (e.g., “Histogram of Quiz Scores”), label the x-axis (“Score”) and y-axis (“Frequency”), and include a suitable scale on the y-axis.

Notes:
- If you prefer finer detail, use smaller bin widths (e.g., 60–64, 65–69, 70–74, 75–79, 80–84, 85–89, 90–94, 95–99) — then recount frequencies accordingly.
- For discrete data with few unique values, a bar chart (bars separated) using the exact scores 60, 75, 80, 95 may be clearer.