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# Three pieces to the package

Q) A while ago you sent me your poem about teaching algebra using envelopes, which I had seen in a previous column. I used this successfully with my adult learners (I work in several community centres in the Midlands). Do you have any poems about the three averages?

A) I have one for mode, another for median and, to complete the package, have written one for mean.

Modern

Most Modern

Determined

By

Mode

The Middle Median Average

Numbers written here and there

Roughly recorded from the paper stare.

The values are written all jumbled

As from the experiment they tumbled.

Central tendency is required

Which one though, you enquired.

Feeling full of doubt

On how to work it out?

Read on for complete coverage

Of calculating median average.

Take each data value

Now arrange them anew,

Order them by their size

So you see the values rise.

The task's diminished

when this is finished.

Cross out equally from either end

Towards the centre you will tend.

14, 15, 16, 16, 20, 20, 20

As other items are shed

The median average is read

A value left in the middle!

Isn't this a diddle!

As you see from this sample

Sixteen is the example.

But what median ensues

When there are two values

Sitting in the middle?

How do we fiddle

To solve this riddle?

The two numbers you add,

Divide this by two and, aren't you glad,

You've a single value coverage

Of this the median average.

Means' Doing Sums

For the average that is really mean,

there's lots of calculations to be seen.

First add all the values of the data

(dividing this answer comes later

using the size of the data sample).

(Have a look at my example).

Total the number of items, that is,

just count.

With this, divide, for the mean

average amount.

Here is an example working out the mean average number of letters per word in the poem "Means Doing Sums". First the number of letters for each word are written down.

5 5 4

3 3 7 4 2 6 4

6 4 2 12 2 2 4

5 3 3 3 6 2 3 4

8 4 6 5 5

5 3 4 2 3 4 6

4 1 4 2 2 7

5 3 6 2 5 4 2 4 5

4 4 6 3 3 4 7 6

To find the total number of letters in the poem, all the values of the words are added together and come to 252. To get the total number of words in the poem, including the title, just count the words, which gives 60.

So the mean average is found by dividing the total number of letters by the total number of words: 252Z60 = 4.2 So on average this poem has about 4.2 letters per word. This doesn't make much sense, because you can't have part of a letter in a word. A better average, in this case, would be the mode.

This can be easily found by creating a stem-leaf plot and looking for the longest "leaf"; in this case 4. So the modal average is 4 letters per word.

The median can also be calculated from this graph as the data is now arranged in order. Counting from either end leaves us with a median of 4 letters per word.

I found this quite interesting when I looked at the overall picture of word length. Just one of 8 letters and one of 12. I wonder if certain types of poems elicit similar patterns, or whether a particular poet has a signature pattern? I don't think so, but it could be a cross-curricular investigation. It seems that I tend to favour four-letter words.

Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses.

www.nesta.org.uk

Email your questions to Mathagony Aunt at teacher@tes.co.uk Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

SOLUTIONS A curious number (Ages 14 to 16). The number is 102,564. You can find this curious number by starting with a dividend of 4 and dividing by 4, adding the digits of the answer to the dividend as you go along. Another curious number is the 18-digit number 105,263,157,894,736,842. When the 2 is moved from the end to the beginning, the new number is twice the original number. The same method can be used to find a 22-digit number ending in 7, such that the new number formed by moving the 7 from the end to the beginning is 7 times the original number.

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