Final answer:
To construct a histogram, divide the data into six intervals (60-69, 70-79, 80-89, 90-99, and 100-109) and plot bars corresponding to the frequency of test scores within each interval on the graph.
Step-by-step explanation:
To create a histogram of the given data, which represents test scores, we will first need to choose the intervals for the scores. Since the question suggests making five to six intervals, let's choose six intervals covering the range of scores from the lowest (65) to highest (98). A suitable scale for these intervals could be: 60-69, 70-79, 80-89, 90-99, rounding up to the nearest whole number to cover the entire range of scores.
Next, we'll count the number of scores in each interval:
- 60-69: 1 score (65)
- 70-79: 3 scores (75, 72, 70)
- 80-89: 4 scores (85, 82, 86)
- 90-99: 4 scores (90, 90, 96, 92)
- 100-109: 1 score (98)
Now, we can sketch the histogram. Label the x-axis with the class intervals and the y-axis with the frequency (the number of scores). For each interval, draw a bar up to the appropriate frequency level.
The bins that contain 80-89 and 90-99 will be the tallest since these contain the most scores. Make sure to use a ruler and pencil to draw straight, even bars, and ensure that all bars are of equal width and are separated by uniform gaps.