# Functional Skills: Comparing Data Sets

## Functional Skills: Comparing Data Sets Revision

**Comparing Data Sets**

Averages and ranges can be used to **compare** different sets of data.

There are **2** skills that you need to learn for comparing data sets.

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

**Skill 1: Comparing Data Sets with Averages**

When we want to **compare** two similar sets of data, there are a few things to consider.

**Example:** the table below displays the sales data from a car dealership across two consecutive weeks.

If we want to compare the sales data across the two weeks, we might want to consider the average (**mean**) number of cars sold each day.

The **mean** for **Week 1** is: \dfrac{12+15+16+13+13+15}{6}=14

The **mean** for **Week 2** is: \dfrac{15+16+10+14+16+25}{6}=16

So the **mean** number of cars sold per day was higher in **Week 2**. Usually we use the **mean **to compare two sets of data, as it takes all of the data into account. However, it is important to note that the mean is affected by outliers – data points which lie far away from the rest of the data. We can see that 25 cars were sold on the Saturday in **Week 2** –Â this is much higher than the rest of the days in **Week 2**, so it increases the mean value significantly.

Instead of using theÂ **mean**, you could compare theÂ **median** or theÂ **modeÂ **for the two weeks. These averages are not affected by outliers, however they do not consider all of the data. There also may not be a **mode** if there are no repeated values.

**Skill 2: Comparing Data Sets with the Range**

The **range** is **not** a type of average, but it is still useful when comparing data. The **range** is the difference between the largest and smallest values in a data set, so it tells us how spread out the data is. If we consider the example of the car sales again,

The **range** for Week 1 is: 16-12=4

The **range** for Week 2 is: 25-10=15

The **range** is smaller for Week 1, so we can say the data is more consistent.

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## Functional Skills: Comparing Data Sets Example Questions

**Question 1:** Two classes sat a maths test. Their marks are summarised in the table below.

Which class had a higher average mark?

**[3 marks]**

Use the mean to compare the average mark for each class.

The mean for **Class 1** is: \dfrac{66+84+37+90+82+45+75+77+63+81}{10}=70

The mean for **Class 2** is \dfrac{80+65+49+50+96+32+83+81+65+69}{10}=67

The mean is higher forÂ **Class 1Â **so we can say it had the higher average mark.

**Question 2:Â **Marvin wants to hire a car for his holiday. There are four car hire companies offering a range of prices, as shown in the table below.

a) Calculate the average cost of a single-day hire and a week-long hire.

b) Calculate the range in the costs of a single-day hire and a week-long hire.

**[4 marks]**

a) The average single day hire cost is:

\dfrac{30+45+24+32}{4}=Â£32.75

The average cost of a week-long hire is:

\dfrac{180+280+150+210}{4}=Â£205

b) The range in cost of a single-day hire is 45-24=Â£21

The range in cost of a week-long hire is 280-150=Â£130

**Question 3:Â **Three athletes compete in a 400 m race. Their times for three heats are shown in the table below.

a) Who had the fastest average time across the three heats?

b) Who had the most consistent times across the three heats?

**[4 marks]**

a) Sharon’s average time is:

\dfrac{52+53+54}{3}=53 s

Miguel’s average time is:

\dfrac{50+49+55}{3}=51.33... s

Dean’s average time is:

\dfrac{58+50+52}{3}=53.33... s

So Miguel had the fastest average time.

b) The range in Sharon’s times is: 54-52=2 s

The range in Miguel’s times is: 55-49=6 s

The range in Dean’s times is: 58-50=8 s

So Sharon had the most consistent times and Dean had the least consistent times across the three heats.

## Functional Skills: Comparing Data Sets Worksheet and Example Questions

### Comparing Data Sets L2

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