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Maths Quiz - Level 5-6 Data Handling - Averages 02 (Questions)

Learn how to calculate the mean from frequency tables. KS3 Maths teaches you how to work out totals and averages when data appears more than once.

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Fascinating Fact:

From a frequency table you can find the mean. Values 2, 3, and 5 with frequencies 4, 3, and 1 give a total of 2×4 plus 3×3 plus 5×1 equals 22. Over 8 items the mean is 2.75.

In KS3 Maths, pupils learn how to calculate averages using frequency tables. Each value in a table may appear more than once, so multiplying by its frequency helps find accurate totals and means.

Key Terms

Frequency: The number of times a value appears in a data set.
Mean: The sum of all values divided by how many there are, considering frequencies.
Data Set: A collection of numbers or information that can be analysed.

Frequently Asked Questions (Click to see answers)

How do you find the mean from a frequency table?

Multiply each value by its frequency, add the totals together, then divide by the total frequency. This gives the mean for all the data combined.

Why is frequency important in averages?

Frequency shows how often each value occurs. Without it, the mean could be misleading because some numbers might appear more than others.

Can you find the median from a frequency table?

Yes. You list the data in order, using the frequencies to repeat values, and then find the middle number in that ordered list.

Try These Related Quizzes

1.

A box of paper clips is labelled 'average contents 100'. How many paper clips would you expect to find in the box?

[ ]	100
[ ]	About 100
[ ]	At least 100
[ ]	More than 100

2.

Which of these is always one of the data values in a set?

[ ]	Mean
[ ]	Median
[ ]	Mode
[ ]	Range

3.

Of 20 customers at a vending machine, 8 spent 50p, 5 spent 60p, 4 spent 75p and 3 spent £1. What was the total amount spent?

[ ]	£2.85
[ ]	£8.50
[ ]	£10.90
[ ]	£13.00

4.

What is the modal amount spent by these 20 customers?

[ ]	50p
[ ]	60p
[ ]	75p
[ ]	£1

5.

What is the median of this data?

[ ]	50p
[ ]	60p
[ ]	75p
[ ]	£1

6.

To find the mean of a data set, add up all values then divide by the .......

[ ]	number of values in the set
[ ]	biggest number in the set
[ ]	smallest value in the set
[ ]	middle value of the set

7.

What is the mean amount spent by the 20 vending machine customers?

[ ]	50p
[ ]	55p
[ ]	60p
[ ]	65p

8.

Which averages could best represent this set of data?

[ ]	Mode and median
[ ]	Mean and mode
[ ]	Median and mean
[ ]	Any of them

9.

The mean length of calls to a help desk is 3 minutes. If the advisers take 1,000 calls, how much time do they spend on the 'phone?

[ ]	20 hours
[ ]	30 hours
[ ]	40 hours
[ ]	50 hours

10.

The mean of the first 9 calls is 5 minutes. The next call takes 10 minutes. What is the mean of the first 10 calls?

[ ]	4.5 minutes
[ ]	5 minutes
[ ]	5.5 minutes
[ ]	6 minutes

You can find more about this topic by visiting BBC Bitesize - Averages

Maths Quiz - Level 5-6 Data Handling - Averages 02 (Answers)

1.

A box of paper clips is labelled 'average contents 100'. How many paper clips would you expect to find in the box?

[ ]	100
[x]	About 100
[ ]	At least 100
[ ]	More than 100

You might get 102 in one box and 98 in another, but the contents should always be about 100

2.

Which of these is always one of the data values in a set?

[ ]	Mean
[ ]	Median
[x]	Mode
[ ]	Range

Remember, the mode is the most common

3.

Of 20 customers at a vending machine, 8 spent 50p, 5 spent 60p, 4 spent 75p and 3 spent £1. What was the total amount spent?

[ ]	£2.85
[ ]	£8.50
[ ]	£10.90
[x]	£13.00

(8 x 0.50) + (5 x 0.60) + (4 x 0.75) + (3 x 1)

4.

What is the modal amount spent by these 20 customers?

[x]	50p
[ ]	60p
[ ]	75p
[ ]	£1

Modal amount = mode (most frequent)

5.

What is the median of this data?

[ ]	50p
[x]	60p
[ ]	75p
[ ]	£1

Both the 10^th and 11^th values are 60p

6.

To find the mean of a data set, add up all values then divide by the .......

[x]	number of values in the set
[ ]	biggest number in the set
[ ]	smallest value in the set
[ ]	middle value of the set

Mean values will often be fractions rather than whole numbers

7.

What is the mean amount spent by the 20 vending machine customers?

[ ]	50p
[ ]	55p
[ ]	60p
[x]	65p

Mean = total ÷ 20. £13.00 ÷ 20 = 0.65

8.

Which averages could best represent this set of data?

[x]	Mode and median
[ ]	Mean and mode
[ ]	Median and mean
[ ]	Any of them

The mean is higher than the amount spent by most customers. 13 of them spent 60p or less

9.

The mean length of calls to a help desk is 3 minutes. If the advisers take 1,000 calls, how much time do they spend on the 'phone?

[ ]	20 hours
[ ]	30 hours
[ ]	40 hours
[x]	50 hours

1,000 x 3 = 3,000 minutes. Divide by 60 to convert to hours

10.

The mean of the first 9 calls is 5 minutes. The next call takes 10 minutes. What is the mean of the first 10 calls?

[ ]	4.5 minutes
[ ]	5 minutes
[x]	5.5 minutes
[ ]	6 minutes

Total call time is (9 x 5) + 10 = 55 so mean is 55 ÷ 10 = 5.5