Organising data & statistical charts · Ages 12–13
Histograms
Bar height = frequency; no gaps between bars.
How to do it
Method
Bar height = frequency; no gaps between bars
The bar from 39.5 to 49.5 is the class 40–49
Another way
Copy it into a table
40–49: 3; 50–59: 7; 60–69: 5
In full
A histogram shows each class's frequency as the height of a bar; the data run on, so the bars have no gaps between them. Read a bar's height across from its top to the scale. The horizontal axis may show the classes (40–49), the class boundaries (39.5, 49.5…, at the bars' edges) or the class marks (44.5, at their middles). With boundaries, the bar from 39.5 to 49.5 is the class 40–49; with marks, the class of mark 44.5 and width 10 is 40–49. The total = the bars' heights added; '50 or more' adds the bar for 50–59 and those after it. Or copy the histogram into a frequency table first, and work from the table.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The histogram shows a team's scores. How many scored 60 or more?
Show the answer and working
Answer: 18
From the class starting at 60, add the heights of it and every bar after: 18.
Example 2
A team of 29 players' scores are shown in the histogram, with one bar covered. How many players are in the covered class?
Show the answer and working
Answer: 9
The covered bar is the class 60–69. The other bars add up to 20: 29 − 20 = 9.
Example 3
The histogram shows a team's scores, its axis marked with class boundaries. More players scored below 89.5 than above it.
True or false?
Show the answer and working
Answer: True
The bars left of 89.5 hold 19; those right of it 7.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The histogram shows a team's scores. How many players are in the team?
Answer:
2.The histogram shows a team's scores. How many scored 70–79?
Answer:
3.The histogram shows a team's scores, its axis marked with class boundaries. The bar from 79.5 to 89.5 is the class –, with players.
Fill in each blank
Answer:
4.The histogram shows a team's scores, its axis marked with class marks; the class width is 10. The class with mark 74.5 has players, and its upper class limit is .
Fill in each blank
Answer:
5.The histogram shows the scores of a team of 25. What percentage of them scored 50 or more?
Answer:
All the answers
- 1. 27
- 2. 1
- 3. 80, 89, 10
- 4. 12, 79
- 5. 88%
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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