How many paper clips would you expect to find in a box labelled 'average contents 100'?

Level 5-6 Data Handling - Averages 02

As part of data handling in KS3 Maths you will have to analyse the information presented to you. One key part of data analysis is finding the averages, There are three main types of average - mean, median and mode.

The whole point of averages is to find a typical or representative value of a data set. But the method you use can affect your results dramatically. The same set of data can give you a mean value of 4.04, a median value of 9 and a mode of 12. You see how much variance there can be? Depending on your data, you will have to decide which method of calculating averages will best represent the information you have. Judgement is a skill which will serve you well in maths.

See how much you know about averages in this quiz. It deals with mean, mode and median. Can you work the averages out? Can you decide which ones best suit different situations? Read the following ten questions carefully and think hard about your answers. Let's see if you can get an above average score of 10-out-of-10! Good luck.

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

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

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

Mean

Median

Mode

Range

Remember, the mode is the most common

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

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

What is the modal amount spent by these 20 customers?

50p

60p

75p

£1

Modal amount = mode (most frequent)

What is the median of this data?

50p

60p

75p

£1

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

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

Mean values will often be fractions rather than whole numbers

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

50p

55p

60p

65p

Mean = total ÷ 20. £13.00 ÷ 20 = 0.65

Which averages could best represent this set of data?

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

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

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

5.5 minutes

6 minutes

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

Author: Frank Evans

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