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Statistical Averages - Mean, Mode and Median - Data36

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The point of using averages is to get a central value of a dataset. The three most common average types are: Mean, Median and Mode.

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Teacher resources for Part 1

Teachers: log in to access the following:

Slides in PPTX (with click-to-reveal answers)

Slides in PDF (one slide per page, suitable for importing into IWB software)

Worksheet (with space for student work)

Handout (slides with exercises only; 4 per page for reduced printing)

Links to past exam and UKMT questions

Teachers: log in to access these.

Visual representation of the mean

Another visual representation of the mean

In the applet below, you can:

adjust the number of values in the set using the slider;

adjust each value in the set using the relevant + or - button; and

click the green button to show the mean and click the pink button to hide the mean.

Consider these questions:

What is the mean of this set of values?

If you add 1 to one of the values, what will happen to the mean?

If you subtract 1 from one of the values, what will happen to the mean?

What do you have to add to any one of the values to increase the mean of the set by 1?

If you add 1 to all of the values what happens to the mean?

If you double all of the values, what happens to the mean?

You want to include an extra value in the list. What does it have to be in order to leave the mean unchanged?

Teacher resources for Part 2

Teachers: log in to access the following:

Slides in PPTX (with click-to-reveal answers)

Slides in PDF (one slide per page, suitable for importing into IWB software)

Worksheet (with space for student work)

Handout (slides with exercises only; 4 per page for reduced printing)

Links to past exam questions

Teachers: log in to access these.

Teachers: log in to view this content.

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Teacher resources for Part 1 Teachers: log in to access the following: Slides in PPTX (with click-to-reveal answers) Slides in PDF (one slide per page, suitable for importing into IWB software) Worksheet (with space for student work) Handout (slides with exercises only; 4 per page for reduced printing) Links to past exam and UKMT questions Teachers: log in to access these.

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S2a – Frequency tables (for Part 2 of this lesson)

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Teacher resources for Part 1

Teachers: log in to access the following:

Slides in PPTX (with click-to-reveal answers)

Slides in PDF (one slide per page, suitable for importing into IWB software)

Worksheet (with space for student work)

Handout (slides with exercises only; 4 per page for reduced printing)

Links to past exam and UKMT questions

Teachers: log in to access these.

Visual representation of the mean

Another visual representation of the mean

In the applet below, you can:

adjust the number of values in the set using the slider;

adjust each value in the set using the relevant + or - button; and

click the green button to show the mean and click the pink button to hide the mean.

Consider these questions:

What is the mean of this set of values?

If you add 1 to one of the values, what will happen to the mean?

If you subtract 1 from one of the values, what will happen to the mean?

What do you have to add to any one of the values to increase the mean of the set by 1?

If you add 1 to all of the values what happens to the mean?

If you double all of the values, what happens to the mean?

You want to include an extra value in the list. What does it have to be in order to leave the mean unchanged?

Teacher resources for Part 2

Teachers: log in to access the following:

Slides in PPTX (with click-to-reveal answers)

Slides in PDF (one slide per page, suitable for importing into IWB software)

Worksheet (with space for student work)

Handout (slides with exercises only; 4 per page for reduced printing)

Links to past exam questions

Teachers: log in to access these.

Teachers: log in to view this content.

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Teacher resources for Part 1 Teachers: log in to access the following: Slides in PPTX (with click-to-reveal answers) Slides in PDF (one slide per page, suitable for importing into IWB software) Worksheet (with space for student work) Handout (slides with exercises only; 4 per page for reduced printing) Links to past exam and UKMT questions Teachers: log in to access these.

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Opinion polls are examples of questionnaires which are used to gauge public opinion. They most used in the run-up to an election to try and forecast who the public will vote for.

This page from Britain Elects shows a time series graph about individual voting intentions for the UK Parliament. The graph is a little more complicated than those you have seen above in a couple of respects:

there are several series: each political party has its own line; and

the time series plotted is a moving average of the previous 7 data points collected—with some further adjustments.

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A knowledge of the four operations from lessons N2a, N2b, N2c and N2d.

S2a – Frequency tables and two-way tables

S2c – Bar charts, vertical line charts and basic histograms

S4a – Median

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N2a – Adding and subtracting positive integers

S2a – Frequency tables and two-way tables

S4a – Median

S4e – Interquartile range and box plots

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N1a – Ordering positive and negative integers

N1b – Ordering decimals

S2a – Frequency tables (for Part 2 of this lesson)

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The median is sometimes a better average to use than the mean, which is another type of average.

Consider two small companies ParCo and OliCo. Each company has one manager and nine other employees. The salaries paid are as follows:

ParCo: The manager earns £50,000 and the other nine employees earn £20,000 each.

OliCo: The manager earns £90,000 and the other nine employees earn £18,000 each.

Imagine both companies are recruiting an extra employee. Would you rather work for ParCo or OliCo?

The mean salary at ParCo is £23,000 compared to £25,200 at OliCo, which makes OliCo look more attractive.

The median salary at ParCo is £20,000 compared to only £18,000 at OliCo, and this makes ParCo look more attractive.

Which type of average is better to use in this case?