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# Functional Skills: Estimating the Mean

FS Level 2AQACity & GuildsEdexcelHighfield QualificationsNCFEOpen Awards

## Estimating the Mean

We are often presented with grouped data in the form of a grouped frequency table. In this instance, we are not dealing with exact values so we can only estimate a value of the mean.

Make sure you are happy with the following topics before continuing.

FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

## Grouped Frequency Tables

Grouped frequency tables are a useful way of displaying broad data by grouping data into classes.

Example:Â the grouped frequency table below shows the number of exercise sessions attended by a group of people.

Note that the classes cannot overlap in a grouped frequency table – be careful when constructing grouped frequency tables not to put the same numbers in twice. For example, if the second class in the example above were $1-2$, someone who attended $1$ exercise session would fit into the first and second class.

In this example, all of the data is known but you may encounter other examples where the last class might say something like ‘$10$ or more’. This would also be useful if the data at the higher end was very spread out.

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## Estimating the Mean

We can use data from grouped frequency tables to estimate the mean value. The reason we are ‘estimating’ is because we do not know how the data is distributed in each class – it could all be at the lower end of the class, all at the higher end or evenly distributed throughout.

We estimate the mean by finding the midpoint of each class and assuming the midpoint to be an average value of each class. We then multiply the midpoint by the frequency, entering the values into a new column.

We can now estimate the mean by taking the total of the Midpoint $\times$ Frequency column and dividing it by the total of the frequency column.

Mean $= 85 \div 34 = 2.5$

So the mean number of exercise sessions attended is $2.5$

FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

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## Functional Skills: Estimating the Mean Example Questions

Question 1:Â $40$ students were asked how many foreign countries they had visited. Their answers are displayed in the grouped frequency table below.

Estimate the mean number of foreign countries visited.

[4 marks]

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First, fill out a new column with the midpoint of each class, then add a new column for the midpoint $\times$ frequency.

The mean is:

$480\div40=12$ countries

Question 2:Â A group of students took a maths test. Their scores are shown in the table below.

Estimate the mean test score.

[4 marks]

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Fill out the midpoint and midpoint $\times$ frequency column. Be careful with the midpoints – they must be exact so in this case we need to use decimals.

We can the estimate the mean as follows:

Mean $= \dfrac{4247.5}{75} = 56.6333....$ marks

If we want to give our answer to a whole number, we can round the mean to $57$ marks.

Question 3: A bakery records the number of cakes it sells each day for a month. Their sales data is shown in the table below.

Estimate the mean number of cakes sold in a day.

[4 marks]

FS Level 2 AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

Fill out a new column for the midpoint and the midpoint $\times$ frequency. Next, find the total of the frequency column and the midpoint $\times$ frequency column:

We can estimate the mean as follows:

Mean $=\dfrac{455}{30}=15.166...$

Rounding the answer to a whole number gives a mean value of $15$ cakes sold per day.

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## Functional Skills: Estimating the Mean Worksheet and Example Questions

### Estimating the Mean L2

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## Related Topics

#### Mean, Median, Mode and Range

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