• From: Mandy Peterson
  • Date: 22 February 1999
  • Subject: Estimating the Mean

I have a question with a table of data with several classes and frequencies. It asks you to estimate the mean.

I know about estimating with calculations so you can do them in your head, but how am I supposed to do questions like these in your head?

Maths Help suggests:

It sounds like you are confused by the word estimate.

This question is not about finding the mean in your head.

To understand why the word 'estimate' is used in this question, consider this example:

Leslie recorded the number of Christmas cards received by everyone in the class:

No. of cards 0-4 5-9 10-14 15-19 20-24
Frequency 3 5 12 6 1

Estimate the mean number of cards.

Notice that the data are grouped. You know that three people received between 0 and 4 cards, but you do not know exactly how many cards each person had.

Because you do not know exactly what the original measurements were, you can only estimate the mean.

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To answer a question like the above, you have probably been taught to draw a table like this:

No. of cards Midpoint (x) Frequency (f) f × x
0-4 2 3 6
5-9 7 5 35
10-14 12 12 144
15-19 17 6 102
20-24 22 1 22
Totals: 27 309

The reason you calculate the mid-point of each group is because you are guessing what the values in each group were.
The best guess is to assume that every one was in the centre of each group. If the measurements are evenly spaced within the group, the variations should even out.

You have only estimated that the class received a total of 309 cards - this may not be the exact total.

The estimate of the mean is 309 ÷ 27 = 11.444... cards per person.

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