Data and probability · Ages 14–15

Averages of grouped data worksheet

Part of: Measures of central tendency

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Data and probability · Ages 14–15

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.The table shows a clinic's patients each day for a month (classes on the left, days on the right). With the class marks, Σ(class mark × frequency) =
Answer:
2.The table shows how many seconds 25 customers queued at a supermarket checkout (classes on the left, customers on the right). What is the estimated mean queuing time, in seconds?
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3.The table shows how many seconds 40 customers queued at a supermarket checkout (classes on the left, customers on the right). What is the estimated mean queuing time, in seconds?
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4.The cumulative frequency polygon shows how many minutes a group of runners took for 10 km. Reading across at half the total frequency, what is the estimated median, to 1 decimal place?
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5.The table is the cumulative frequency table of how many minutes 25 members of a gym spend on a workout (classes on the left, cumulative frequencies on the right). What is the estimated mean workout time, in minutes?
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6.The table is the cumulative frequency table of how many minutes 40 members of a gym spend on a workout (classes on the left, cumulative frequencies on the right). What is the estimated mean workout time, in minutes?
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7.The table shows how many minutes each visitor stayed in a park one day (classes on the left, visitors on the right). Which is the modal class?
- A. 60–69
- B. 90–99
- C. 70–79
- D. 80–89
Choose the right answer
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8.The table shows 25 families' grocery spending in a week ($, classes on the left, families on the right). The estimated mean spending is $72.4.
True or false?
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9.The table shows the audience at each showing in a cinema for a month (classes on the left, showings on the right). Which class holds the median?
- A. 100–109
- B. 80–89
- C. 70–79
- D. 90–99
Choose the right answer
Answer:
10.The table shows 20 families' grocery spending in a week ($, classes on the left, families on the right). The estimated mean spending is $68.
True or false?
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11.The table shows 20 families' grocery spending in a week ($, classes on the left, families on the right). The estimated mean spending is $230.
True or false?
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12.The table shows 20 families' grocery spending in a week ($, classes on the left, families on the right). The estimated mean spending is $41.25.
True or false?
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13.The cumulative frequency polygon shows how many minutes 37 cyclists took for a hill route. What is the estimated median time, in minutes, to 1 decimal place?
Working:
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14.The table shows what each of 27 customers spent ($) at a snack shop one day (classes on the left, customers on the right). Using the class marks, about how many dollars did all the customers spend that day?
Working:
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15.The table shows how many minutes 25 passengers waited at a bus stop (classes on the left, passengers on the right). With the class marks: Σ(class mark × frequency) = , and the estimated mean wait is minutes.
Fill in each blank
Working:
Answer:
16.The table shows how many people used a gym on each of 22 days (classes on the left, days on the right). The modal class's lower limit is , and the lower limit of the class holding the median is .
Fill in each blank
Working:
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17.The table shows how many people used a gym on each of 29 days (classes on the left, days on the right). The modal class's lower limit is , and the lower limit of the class holding the median is .
Fill in each blank
Working:
Answer:
18.The table shows what each of 31 customers spent ($) at a snack shop one day (classes on the left, customers on the right). Using the class marks, about how many dollars did all the customers spend that day?
Working:
Answer:

Show the answers and working

Averages of grouped data worksheet: Answers and working

1. 1054
The class marks are 42, 47, 52, 57, 62; each times its frequency, added: 1054.
2. 61.4 s
Let each class mark stand for its class: Σ(class mark × frequency) = 1535; over 25: 1535 ÷ 25 = 61.4 s.
3. 74.75 s
Let each class mark stand for its class: Σ(class mark × frequency) = 2990; over 40: 2990 ÷ 40 = 74.75 s.
4. 29.5 minutes
Half the total is 20; across at that height to the curve and down gives 29.5 minutes (in proportion along that straight stretch).
5. 33 minutes
First subtract neighbouring cumulative frequencies to get the frequencies back, 6, 5, 2, 2, 10; the class marks are 22, 27, 32, 37, 42: Σ(class mark × frequency) = 825, and 825 ÷ 25 = 33 minutes.
6. 62.75 minutes
First subtract neighbouring cumulative frequencies to get the frequencies back, 6, 12, 2, 10, 10; the class marks are 52, 57, 62, 67, 72: Σ(class mark × frequency) = 2510, and 2510 ÷ 40 = 62.75 minutes.

7. A. 60–69
60–69 has the highest frequency (12), so it is the modal class.
8. True
With the class marks: Σ(class mark × frequency) ÷ 25 = 72.4.
9. C. 70–79
42 showings, so the median is the (42 + 1) ÷ 2-th; adding the frequencies class by class, it falls in 70–79.
10. True
With the class marks: Σ(class mark × frequency) ÷ 20 = 68.
11. False
With the class marks: Σ(class mark × frequency) ÷ 20 = 57.5.
12. False
With the class marks: Σ(class mark × frequency) ÷ 20 = 43.25.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 70.3 minutes
Half the total is 18.5: across at that height to the curve and down, about 70.3 minutes.
14. 1934 dollars
Each class mark stands for every customer in its class: Σ(class mark × frequency) = $1,934.
15. 985, 39.4
Class marks 32, 37, 42, 47, 52, each times its frequency, added: 985; 985 ÷ 25 = 39.4.
16. 35, 40
The most frequent class starts at 35; with 22 days, the (22 + 1) ÷ 2-th value falls in the class starting at 40.
17. 45, 45
The most frequent class starts at 45; with 29 days, the (29 + 1) ÷ 2-th value falls in the class starting at 45.
18. 1479.5 dollars
Each class mark stands for every customer in its class: Σ(class mark × frequency) = $1,479.5.

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