Organising data & statistical charts · Ages 12–13
Grouped frequency tables
Classes neither overlap nor leave gaps; frequencies add to the total.
How to do it
Method
Classes neither overlap nor leave gaps; frequencies add to the total
60 or more: 5 + 4 + 1 = 10 people
Another way
Count class by class
Count all the values in the 40s: 3
In full
To group data: look at the least and greatest values, choose a class width, say 10, so the classes 40–49, 50–59, 60–69… run from small to large, without overlapping or leaving gaps, and take in every value. Then tally each value into its class, count each class's frequency, and check that the frequencies add up to the number of data. Or count class by class: how many values are in the 40s, then the 50s, and so on. Reading the table: '60 or more' adds the frequencies of 60–69, 70–79…; a percentage = that frequency ÷ the total × 100%. Once grouped, a value is known only by its class, not exactly.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The table tallies how many skips each member of a skipping team made in a minute (the left column is skips). How many made 30–39 skips?
Show the answer and working
Answer: 11
The row 30–39 has 11 marks (each four-and-a-bar is 5): 11 members.
Example 2
Tsz-hin records 12 players' scores: 53, 75, 46, 71, 51, 47, 73, 61, 55, 54, 50, 66. The frequencies of the classes 40–49, 50–59, 60–69 and 70–79 are , , and .
Fill in each blank
Show the answer and working
Answer: 2, 5, 2, 3
Tally each score into its class and count: 2, 5, 2, 3, adding up to 12.
Example 3
A set of data runs from 34 to 63. Grouping them in classes of width 10, which grouping is suitable?
- A. 30–38、40–48、50–58、60–68
- B. 40–49、50–59、60–69、70–79
- C. 30–39、40–49、50–59、60–69
- D. 30–40、40–50、50–60、60–70
Choose the right answer
Show the answer and working
Answer: C. 30–39、40–49、50–59、60–69
Classes must run from small to large, not overlap, leave no gaps, and take in all the data from 34 to 63: 30–39, 40–49, 50–59, 60–69.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.The table is a grouped frequency table of how many skips each member of a skipping team made in a minute (the left column is skips, the right members). How many members are in the team?
Answer:
2.The table is a grouped frequency table of a team's weights in kg (the left column is weight, the right players). Which class has the most players?
- A. 60–69
- B. 80–89
- C. 70–79
- D. 50–59
Choose the right answer
Answer:
3.A team has 25 members. The table is a grouped frequency table of their skips in a minute (the left column is skips, the right members). What percentage of the team made 60 skips or more?
Answer:
4.A set of data runs from 21 to 54. Grouping them in classes of width 10, which grouping is suitable?
- A. 30–39、40–49、50–59、60–69
- B. 20–29、30–39、40–49、50–59
- C. 20–28、30–38、40–48、50–58
- D. 20–30、30–40、40–50、50–60
Choose the right answer
Answer:
5.A team has 33 members. The table is a grouped frequency table of their skips in a minute (the left column is skips, the right members). What is the '?' in the table?
Answer:
All the answers
- 1. 23
- 2. C. 70–79
- 3. 48%
- 4. B. 20–29、30–39、40–49、50–59
- 5. 3
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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