Introducing S1 © Christine Crisp “Teach A Level Maths” Statistics 1.

Introducing S1Introducing S1

© Christine Crisp

““Teach A Level Teach A Level Maths”Maths”

Statistics 1Statistics 1

Introducing S1

Statistics 1

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Introducing S1

The word “statistics” is used in 2 ways:

• Statistics is the branch of mathematics which deals with data. We form mathematical models to predict from the data and to say how accurate our predictions are likely to be.

• A statistic is a number calculated from a sample, for example the mean.

Introducing S1

As part of GCSE you studied Data Handling and met some calculations and diagrams that can be used to summarize data.

This module starts by reminding you about the calculations and diagrams.

We then extend the calculations and study some statistical models.

Introducing S1

These presentations explain the theory. You don’t need to copy it all down as there is a summary from time to time.

The notepad symbol is used for a key example or summary and I am suggesting you do copy this down. Your teacher may also give you other notes or the print-outs from the end of each file.

When you see the calculator symbol do the calculation yourself.

I use the open book symbol for exercises and also to ask you to use your statistical tables.

Introducing S1

to have your calculator in every lesson,

Two essentials for learning Statistics are . . .

to have your booklet of formulae and tables in every lesson.

We’ll start with revising measures of location. Don’t worry if you haven’t met the phrase before as you’ll certainly know the measures.

Measures of Location

Measures of location give us an idea about the size of numbers in a set of data.

The following are all measures of location:

meanmedianmode

the three ms

The mean is the arithmetic average. The median is the value in the middle of a set of ranked data ( data that are in numerical order ).

The mode is the value that occurs most often in a set of data.

median:middlemode: most


e.g. Find (a) the mean, (b) the median and (c) the mode, of the data below.

3 8 8 8 9 10 11 15 18

Solution:

9

15111098883 18Mean =

Median =

10



1815111098883

Solution:

9

15111098883 18Mean =

9Median =

Mode =

10



1815111098883

So, the mean and median tell us the numbers are located around 10 or 9 and the mode tells us that there are more 8s than any other number.

Suppose we now change the final data item from 18 to 81.

Solution:

9

15111098883 18Mean =

9Median =

Mode =8

10



Solution:Mean =

9

15111098883

9Median =

3 8 8 8 9 10 11 15 81

Mode =8

17

The mean has increased from 10 to 17 but the median and mode are unchanged.

81

One advantage of the mode and median as measures of location is that they are unaffected by an extreme value.One advantage of the mean is that it includes all the data.


Other measures of location are the percentiles.These are the percentages of the data set. So, the 10th percentile is the observation that is 10% of the way through the data ( when the data are in numerical order ).

The most important percentiles are the 50th, which is the median, the 25th, called the lower quartile (LQ) and the 75th, called the upper quartile (UQ).


SUMMARY The mean is the arithmetic average.

The median is the value in the middle of a set of ranked data ( data that are in numerical order ). The mode is the value that occurs most often in a set of data.


One advantage of the mode and median as measures of location is that they are unaffected by extreme values.

One advantage of the mean is that it includes all the data.

Measures of Spread

Measures of spread, or dispersion, give us a way of measuring the variability within a data set.

The range is one measure of dispersion but it uses only 2 values, the smallest and largest, so is greatly affected by extreme values.

The interquartile range (IQR) is much more useful as it measures the spread of the middle 50% of the data. We will see how to find it in the presentation on stem and leaf diagrams.

The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.


The word “statistics” is used in 2 ways:

• Statistics is the branch of mathematics which deals with data. We form mathematical models to predict from the data and to say how accurate our predictions are likely to be.

• A statistic is a number calculated from a sample, for example the mean.


Measures of location give us an idea about the size of numbers in a set of data.

The following are all measures of location:

meanmedianmode

the three ms

The mean is the arithmetic average. The median is the value in the middle of a set of ranked data ( data that are in numerical order ).

The mode is the value that occurs most often in a set of data.


SUMMARY The mean is the arithmetic average.

The median is the value in the middle of a set of ranked data ( data that are in numerical order ). The mode is the value that occurs most often in a set of data.


An advantage of the mode and median as measures of location is that they are unaffected by an extreme value.

An advantage of the mean is that it includes all the data.

Measures of Spread

Measures of spread, or dispersion, give us a way of measuring the variability within a data set.

The range is one measure of dispersion but it uses only 2 values, the least and greatest, so is greatly affected by extreme values.

The interquartile range (IQR) is much more useful as it measures the spread of the middle 50% of the data. We will see how to find it in the presentation on stem and leaf diagrams.

Introducing S1 © Christine Crisp “Teach A Level Maths” Statistics 1.

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Transcript of Introducing S1 © Christine Crisp “Teach A Level Maths” Statistics 1.