Week 12 Β· Making histograms, box plots and choosing a display Β· 3 lessons
1
Building a histogram from raw data
Discover Mathematics P6: Term 1, Unit 6, Lessons 3β5
GoalChoose equal intervals, count the data, draw a histogram and describe its shape.
New words
raw data Β· the numbers exactly as we collected theminterval width Β· the size of each interval, the same for all of themfrequency table Β· a table that shows how many values fall in each intervalshape Β· how the bars rise and fall: peak, tail, symmetric or skewed
Explanation
To build a histogram from raw data, follow five steps. First find the smallest and the largest value. Second choose one interval width, so that you get about four to six intervals. Third write the intervals so that they do not overlap, for example 0β4, 5β9, 10β14. Fourth count how many values fall in each interval and write them in a frequency table; the counts must add up to the number of data values. Fifth draw one bar for each interval, with the height equal to the count. Then describe the shape: where is the peak, is there a long tail, is it symmetric? The width matters: very narrow intervals give too many small bars, and very wide intervals hide the shape.
β Remember
Find min and max β choose a width β write equal intervals β count β draw the bars. Check: the counts add up to the number of values.
Worked examples
Stickers
Pupils
0β4
3
5β9
7
10β14
6
15β19
3
20β24
1
Twenty pupils counted their stickers: 3, 12, 7, 15, 9, 4, 18, 11, 6, 13, 8, 22, 10, 5, 14, 9, 16, 2, 12, 7. The smallest is 2 and the largest is 22, so the width 5 gives five intervals. We count each interval and check: 3 + 7 + 6 + 3 + 1 = 20.
We draw the histogram. The peak is the interval 5β9, with 7 pupils. The bars fall slowly to the right, and one pupil is alone in 20β24, so the shape is skewed right: most pupils have fewer than 15 stickers.
What if we choose a wider interval of 10? The same data give 10 pupils in 0β9, 9 in 10β19 and 1 in 20β29. Only three bars are left, and the peak at 5β9 can no longer be seen. A good width keeps the shape visible.
Class activity
Class histogram. Collect twelve numbers that are easy to get at home, for example the number of steps from your bed to the kitchen as counted by your family members, or the age of twelve relatives. Choose an interval width, make a frequency table and draw the histogram on squared paper. Describe the shape in one sentence.
Practice
1
Fifteen pupils gave the minutes they spend on homework: 25, 40, 35, 50, 30, 45, 20, 35, 40, 55, 30, 25, 45, 35, 60. Make a frequency table with the intervals 20β29, 30β39, 40β49, 50β59, 60β69.
