Functional Skills: Comparing Data Sets

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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.

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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 – this is much higher than the rest of the days in Week 2, so it increases the mean value significantly.

Instead of using the mean, you could compare the median or the mode 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.

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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

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 for Class 1 so we can say it had the higher average mark.

a) The average single day hire cost is:

 

\dfrac{30+45+24+32}{4}=£32.75

 

The average cost of a week-long hire is:

 

\dfrac{180+280+150+210}{4}=£205

 

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

 

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

 

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.

Additional Resources

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Exam Tips Cheat Sheet

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Formula Booklet

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Functional Skills: Comparing Data Sets Worksheet and Example Questions

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Comparing Data Sets L2

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