Statistics 2
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Statistics 2. Quantitative (Numerical) (measurements and counts). Qualitative (categorical) (define groups). Continuous. Discrete. Categorical (no idea of order). Ordinal (fall in natural order). We are only going to consider quantitative variables in this AS. Variables.

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Statistics 2

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Statistics 2

Statistics 2


Statistics 2

Quantitative

(Numerical)

(measurements and counts)

Qualitative

(categorical)

(define groups)

Continuous

Discrete

Categorical

(no idea of order)

Ordinal

(fall in natural order)

We are only going to consider

quantitative variables in this AS

Variables


Quantitative

Discrete

Many repeated values

Age groups

Marks

Continuous

Few repeated values

Height

Length

Weight

Quantitative


Qualitative

Categorical

Gender

Religious denomination

Blood types

Sport’s numbers (e.g. He wears the number ‘8’ jersey)

Ordinal

Grades

Places in a race (e.g. 1st, 2nd, 3rd)

Qualitative


Collecting data

Tally charts

Stem and leaf plots

Collecting data

How we collect the data usually depends on what question we wish to answer.


Tally chart

Tally chart

  • If we were asking people what they had for breakfast we might set up a table like this…


Tally chart1

Tally chart


Tally chart2

Tally Chart

  • We use a tally chart when data fits easily into categories.


Stem and leaf plot

Stem and leaf plot

  • A stem and leaf plot sorts data that has few values the same.


Example

Example

  • The number of punnets of strawberries picked by Carol over a 17-day period. (This example is in your text book)

  • 65 73 86 90 99 106 45 92 94 102 107 107 99 83 101 91


Example1

Example

  • Set up a ‘stem’ based on the fact that the numbers picked are between 40 and 110


Example2

Example


Example3

Example

  • The first number is 65 and the next is 73.

  • They are recorded like this


Example4

Example


Example5

Example


Sort the data in order

Sort the data in order


Lowest and highest values

Lowest and highest values


Median and quartiles

Median and quartiles


Median and quartiles1

Median and quartiles


Median and quartiles2

Median and quartiles

  • 5- number summary

  • Lowest = 45

  • LQ = 84.5

  • Median = 94

  • UQ = 101.5

  • Highest = 107


Pictures that tell a story

Pictures that tell a story

  • Drawing a picture of our data.

  • Our data is discrete and hence a bar graph is an appropriate way of showing our ‘picture’.


A bar graph

A bar graph


A bar graph1

A bar graph

  • We use a bar graph (spaces between bars) because we are dealing with discrete data (counted data, many repeated values)


Bar graph

Bar graph

  • A bar graph gives us a picture of the data and we can easily see many features of our data.


Bar graph1

Bar graph

  • Lowest = 3 letters

  • Highest = 8 letters

  • Mode = 5 letters

  • The graph is approximately symmetrical and uni-modal (has only one mode)


Bar graph2

Bar graph

  • To find out how many were surveyed, you add the frequencies together.


Pie graph

Pie graph

  • Each category makes up a certain percentage of the ‘pie’.

  • A pie graph does not tell us how many were in the data set.

  • You must be careful when comparing data from 2 pie graphs.


Pie graph1

Pie graph


Pie graph2

Pie graph


Pie graph3

Pie Graph

  • This also is an appropriate graph as it shows the relative numbers in each category.

  • It does not give us a lot of specific information like how many were surveyed or how many had 8 letters in their name.


Box and whisker plot

Box and Whisker plot

  • The box and whisker plot is a picture of the 5-number summary and it shows us where the cut-off is for every quarter of the data.

  • Again, the box and whisker plot does not tell us how many were in the sample just how the quarters were distributed.


Box and whisker plot1

Box and Whisker plot


Box and whisker plot2

Box and Whisker plot

  • This gives us a lot of information.

  • The lowest and highest values.

  • The median, upper and lower quartiles.

  • We also get a sense of how the data is distributed.


Box and whisker plot3

Box and Whisker Plot

  • Box and whisker plots can also be used to compare two sets of data.


Back to strawberry picking

Back to strawberry picking!

  • Who would you employ?


Strawberry picking

Strawberry picking


Comparing

Comparing


Comparing1

Comparing

  • Carol has the higher mean.

  • Dilip has the higher median.

  • Carol has the higher mode.


Central tendency

Central tendency

  • Which central tendency is more useful in measuring the punnets picked overall?


Comparing2

Comparing


Comparing3

Comparing

  • Carol has the lower range.

  • Dilip has the lower interquartile range.

  • Carol’s lowest value is higher than Dilip’s.

  • Dilip’s highest value is higher than Carol’s.


Spread

Spread

  • Which picker is more reliable?


Back to the data

Back to the data


Comparing using a picture

Comparing using a picture


Box and whisker

Box and whisker


Box and whisker1

Box and whisker

  • Overall they both picked roughly the same number of punnets.

  • Carol 1537

  • Dilip 1532


Box and whisker2

Box and whisker

  • The long tails on the box and whisker plots suggest outliers (extreme values).

  • 45 is a likely outlier for Carol and suggests she worked a half day.

  • 0 suggests that Dilip did not work on one of the days which would have pulled his mean value down.

  • 49 is also an outlier for Dilip suggesting he also worked half a day.


Box and whisker3

Box and whisker

  • Dilip is more reliable as his spread as shown by the interquartile range is smaller.

  • (This is presuming he doesn’t just take days off when he wants to.)


What not to do

What not to do!!!


No no no this is not a good idea

No! No! No!- this is not a good idea!


No no no this is not a good idea1

No! No! No!- this is not a good idea!

  • Axes need to be labelled.

  • Colour distorts the graph.

  • Lines also distort the graph- take a look at these.


Are the lines parallel

Are the lines parallel?


Are these lines parallel

Are these lines parallel?


Are these lines parallel1

Are these lines parallel?


Are the lines parallel1

Are the lines parallel?


Statistics 2

  • This kind of graph gives us very little information.


Negatively skewed unimodal

Negatively skewed (unimodal)


Positively skewed

Positively skewed


Symmetric

Symmetric


Uniform

Uniform


Groupings bimodal

Groupings (bimodal)


Outlier

Outlier


Bi variate data

Bi-variate data

  • Looking for relationships between two variables.


Example6

Example

  • Is there a relationship between the amount of study a person does and their test result?


Consider data on hours of study vs test score

Consider data on ‘hours of study’ vs ‘ test score’


Relationship

Relationship

  • There is a positive linear relationship between the amount of study and the test score. This means that as the hours of study increases, we expect an increase in test score.


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