Cumulative frequency & charts · Ages 13–14
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 table is drawn as a histogram (the left column is scores, the right players). The bar for 40–49 runs along the axis from to , and is tall.
Fill in each blank
Show the answer and working
Answer: 39.5, 49.5, 1
The bar runs from the lower boundary 39.5 to the upper 49.5, as tall as the frequency 1.
Example 2
The histogram shows a team's scores. From it we can be sure that at least 26 players scored 54 or more.
True or false?
Show the answer and working
Answer: True
Only the 26 scoring 60 or more are certain (the class holding 54 might all be under it). We can be sure only if 26 is no more than 26.
Example 3
The histogram shows the scores of a team of 25. What percentage of them scored 50 or more?
Show the answer and working
Answer: 48%
50 or more: 12 players; 12 ÷ 25 × 100% = 48%.
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. At least how many players scored 57 or more?
Answer:
2.The histogram shows a team's scores. From it we can be sure that at least 4 players scored 51 or more.
True or false?
Answer:
3.These 10 values are grouped and drawn as a histogram: 44, 58, 32, 52, 44, 22, 64, 24, 35, 62. How tall is the bar for 30–39?
Answer:
4.The histogram shows a team's scores. At most how many players scored 68 or more?
Answer:
5.The histogram shows a team's scores, its axis marked with class boundaries. More players scored below 49.5 than above it.
True or false?
Answer:
All the answers
- 1. 5
- 2. True
- 3. 2
- 4. 15
- 5. True
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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