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Using Calculators to Find Averages (Cambridge (CIE) IGCSE International Maths)

Revision Note

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Cambridge (CIE) International Maths: ExtendedCambridge (CIE) International Maths: Core

Using Calculators to Find Averages

How do I use my graphic display calculator to find averages for raw data?

  • You can use your graphic display calculator to help you to find the quartiles and averages for a set of raw data

    • For example, you may have been given a list of times that a group of 5 people took to run 100 m

  • Enter the raw data into the first column of a spreadsheet on your graphic display calculator

    • It is a good idea to label the column (if possible) e.g. Time

    • Some calculator models will use a statistics mode instead, where you can enter the data in a table

  • Select the statistics function and perform the statistics calculations for one-variable statistics

    • You need to make sure that the frequency is set to '1'

    • You may need to find the settings menu to change this

  • Your graphic display calculator will display various statistical measures including:

    • Mean, x with bar on top

    • Median, MedianX or Med

    • Lower quartile, straight Q subscript 1 straight X or simply straight Q 1

    • Upper quartile, straight Q subscript 3 straight X, or simply straight Q 3

Examiner Tips and Tricks

  • Make sure you know how to use the statistics function on your particular graphic display calculator model

How do I use my graphic display calculator to find averages for data in a frequency table?

  • You may be asked to find a particular average from a set of data that has been given to you in the form of a frequency table

Number of siblings

Frequency

0

4

1

8

2

6

3

2

  • When entering data from a frequency table to a spreadsheet or table on your graphic display calculator, you need to use two columns

    • Enter the data item into the first column

      • Label the column, e.g. siblings

    • Enter the corresponding frequency into the second column

      • Label the column, e.g. freq

  • Select the statistics function and perform the statistics calculations for one-variable statistics

    • You will need to specify which column contains the data and which contains the frequency

      • You may need to find the settings menu to change this

      • Some calculator models will refer to the columns as lists

  • Your graphic display calculator will display various statistical measures including:

    • Mean, x with bar on top

    • Median, MedianX or Med

    • Lower quartile, straight Q subscript 1 straight X or simply straight Q 1

    • Upper quartile, straight Q subscript 3 straight X, or simply straight Q 3

Examiner Tips and Tricks

  • If your calculator is able, labelling the columns in a spreadsheet is a good idea

    • This will make it easier to remember which is the data and which is the frequency

Worked Example

Using your calculator, find the median and the upper and lower quartiles for the data set given below.

 43                        29                        70                        51                        64                       43

Enter the raw data as a list into a spreadsheet or table on your graphic display calculator
Label the list 'data'

data

43

29

70

51

64

43

Select the statistics calculations from the statistics function and choose one-variable statistics

Make sure the frequency is set to '1'

Read off the values for the median (MedianX or Med), the lower quartile (straight Q subscript 1 straight X or straight Q 1) and the upper quartile (straight Q subscript 3 straight X or straight Q 3)

Median = 47
Lower quartile = 43
Upper quartile = 64

How do I use my graphic display calculator to find averages for grouped data?

  • You may be asked to find a particular average from a set of data that has been grouped

Length (cm)

Frequency

0 less than space l space less or equal than 5

13

5 less than space l space less or equal than 10

27

10less than space l space less or equal than 15

19

15less than space l space less or equal than20

8

  • You cannot enter a 'group', you must assume a value for each item in a particular group

    • Assume each data item in the group to be the midpoint of the group

  • To find the midpoint of a group

    • Add the two end points of the group together and halve

    • E.g. For the group 5 less than l less or equal than 10, the midpoint is fraction numerator 5 plus 10 over denominator 2 end fraction equals 7.5

  • It is useful to add the midpoint as an extra column in the table

Length (cm)

Frequency

Midpoint

0 less than space l space less or equal than 5

13

2.5

5 less than space l space less or equal than 10

27

7.5

10less than space l space less or equal than 15

19

12.5

15less than space l space less or equal than20

8

17.5

  • When entering data from a grouped frequency table to a spreadsheet on your graphic display calculator, you need to use two columns

    • Enter the data item into the first column

      • The data item will be values from the midpoint column

      • Label the column, e.g. length

    • Enter the corresponding frequency into the second column

      • Label the column, e.g. freq

  • Select the statistics function and perform the statistics calculations for one-variable statistics

    • You will need to specify which column contains the data and which contains the frequency

      • You may need to find the settings menu to change this

      • Some calculator models will refer to the columns as lists

  • Your graphic display calculator will display various statistical measures including:

    • Mean, x with bar on top

    • Median, MedianX or Med

    • Lower quartile, straight Q subscript 1 straight X or simply straight Q 1

    • Upper quartile, straight Q subscript 3 straight X, or simply straight Q 3

Examiner Tips and Tricks

  • Whilst you can use your calculator to find the statistical measures, you should still write down any supporting working

    • E.g. Writing down the midpoints when dealing with grouped data can be worth a method mark

    • How many marks a question is worth can help indicate how much working is expected

      • If it is only 1 mark, it is likely you can just use your calculator to find the answer!

Worked Example

A number of elephants drink at a particular waterhole.

The length of time that they spend at the waterhole one morning is recorded by a researcher and recorded in the following table:

Time, t (mins)

0 less or equal than t less than 15

15 less or equal than t less than 30

30 less or equal than t less than 45

45 less or equal than t less than 60

Frequency, f

5

8

6

2

Use your calculator to calculate an estimate for the mean time spent by an elephant at the waterhole.

Add another row to the table for the midpoints

Time, t (mins)

0 less or equal than t less than 15

15 less or equal than t less than 30

30 less or equal than t less than 45

45 less or equal than t less than 60

Frequency, f

5

8

6

2

Midpoint

fraction numerator 0 plus 15 over denominator 2 end fraction equals 7.5

fraction numerator 15 plus 30 over denominator 2 end fraction equals 22.5

fraction numerator 30 plus 45 over denominator 2 end fraction equals 37.5

fraction numerator 45 plus 60 over denominator 2 end fraction equals 52.5

Enter the data into a spreadsheet on your graphic display calculator
Add the 'Midpoint' values to the first column, label the list 'time'
Add the 'Frequency, f' values to the second column, label the list 'freq'

time

freq

7.5

5

22.5

8

37.5

6

52.5

2

Select the statistics calculations from the statistics function and choose one-variable statistics

Make sure the data is set as the 'time' column
Make sure the frequency is set to the 'freq' column

Read off the values for the mean (x with bar on top)

Mean = 26.07142...

Round to 3 significant figures

Mean = 26.1 minutes

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    Author
    Reviewer
    Naomi C

    Author: Naomi C

    Expertise: Maths

    Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.