Everyday maths for Health and Social Care and Education Support 1

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# 7 Averages

Sometimes it’s easier to present data numerically rather than graphically, and to find one number to represent a collection of data instead of lots of numbers. You can do this by finding the arithmetical average: ‘arithmetical’ means ‘doing sums’, and the ‘average’ is the representative value of all our data. So working out the arithmetical average means working out a representative value for your data with mathematical calculations.

Note: With data we talk about ‘data sets’, or sets of data. ‘Sets’ is just another word for ‘group’. So if we carried out a survey, we would have a data set.

You’ll be familiar with the word ‘average’. Outside maths, it is used to mean ‘not special’ or ‘just OK’. But in maths, ‘average’ means we can have one value that is representative of all our data and that uses all our data. You will also encounter the terms ‘mean average’, or just ‘mean’. The mean average is what we are referring to in this course and what we show you how to calculate below.

Where do we find averages in real life?

• Average number of calories a person consumes each day.
• Average life expectancy.
• Average speed of an ambulance journey.
• Average number of portions of fruit and vegetables a person consumes each day.
• Average reading age of students in a class.

The arithmetic average is not difficult to work out. You need to do the following.

1. Add up all your data to a total. In the first example in the list above, about the number of calories consumed each day, this could be the total number of calories consumed in one week (let’s call this total ‘W’).
2. Add up the number of categories that your data falls into. Using the same example, this would be the number of days in a week.
3. Divide the total of your data (W) by the number of bits of data (7). So W ÷ 7 = the average. In the example about the average number of calories consumed each day, if there were 12,600 total calories consumed in the week, divided by 7, the average number of calories consumed would be 1800 each day.

Have a look at the example below, where you will be looking at the average number of calories consumed.

## Example: Average number of calories consumed

Jon recorded his daily calorie consumption for one week as follows:

DayNo. of calories consumed
Sunday2,100
Monday2,400
Tuesday2,000
Wednesday2,200
Thursday2,350
Friday1,950
Saturday2,240

You could draw a bar chart or a line graph to present this data. However the number of calories consumed varied a lot from day to day.

It might be more useful to find out the average number of calories consumed per day. This would give you one value, which you could use as a guide as to whether Jon is consuming too many or too few calories overall.

### Method

To work out this average value you need to:

• add up the amount of calories for each day
• divide this by the number of days you have the data for.

With this example we have:

• 2,100 + 2,400 + 2,000 + 2,200 + 2,350 + 1,950 + 2,240 = 15,240 calories for the week

and seven days of data. So, the average is:

• 15,240 ÷ 7 = 2,177 calories (to the nearest whole number)

Note: You must remember what units you are working in and write in these units after your average value – otherwise, it won’t make sense.

The NHS recommends that a man should consume around 2,500. Jon’s average daily calorie consumption of 2,177 would suggest that he is consuming too few calories. However, 2,500 calories is only a recommendation and is affected by many factors such as age and levels of physical activity. Hence, as long as Jon is maintaining a healthy weight, his doctor or nurse may decide that his daily calorie consumption is appropriate and healthy for him.

### Method summary

• Find out the number of categories that your data falls into.
• Divide the total of your data by the number of categories of data to give the average.
• Don’t forget to put what units you are working in, for example hours, goals, people, etc.
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