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

# A starting point

# Part 1 – Finding the mean from a list

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### Visual representation of the mean

### Another visual representation of the mean

- 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?

# Working with the mean with minimal calculation

In this activity, students cannot work out the mean length of any of the sets of pencils, because no lengths are given. They should however, be able to to answer the questions posed. In the first case, it should be evident that the mean length of pencil is greater in set A than set B, since both have the same number of pencils but those in set A have a greater total length.

In the second question, you could position the strip of paper in line with the pencils in set D, and determine how the total length of the two pencils and paper compares to the four pencils in set C.

In the third question, the strip of paper could be folded into quarters (by folding in half and then half again). It could then be unfolded partially so that it is three-quarters of the length of the pencils in set E. This can then be compared with the total length of the pencils in set F.

# Part 2 – Mean from a frequency table

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# Cross-curricular link: waste management

At the point of final treatment, the total waste generated in the UK in 2016 weighed 214.3 million tonnes.

This figure is from the UK government.

- Based on an approximate population of 65 million, what is the mean mass of waste produced by each person? Does this figure seem unexpectedly high or low? Why might this be?

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