Topic: Data Handling

LO: To be able to understand and produce box plots.

STARTERPREPARE FOR LEARNING

AGREE LEARNING OBJECTIVES

Calculate the median of these numbers:5, 7, 3, 6, 10, 4, 8, 7, 73, 4, 5, 6, 7, 7, 7, 8, 1011, 8, 9, 10, 3, 6, 8, 103, 6, 8, 8, 9, 10, 10, 11

BOXPLOTS

PRESENT NEW INFO

Quartiles

• The quartiles split the data into quarters.

• The lower quartile is a ¼ of the way into the data

• The upper quartile is ¾ of the way into the data

• The median is (i.e. ½) of the way into the data

CONSTRUCT MEANING

Quartiles

• Here are the maths test results of 23 male students:

3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10

• Lower Quartile: = = = 6th = 4• Median: = = = 12th = 7• Upper Quartile: 3 x LQ = 18th = 9

CONSTRUCT MEANING

Quartiles• Below are the ages of 15 members of a golf club.

Calculate the median and quartiles for the data.

• Lower Quartile: = = = 4th = 24• Median: = = = 8th = 33• Upper Quartile: 3 x LQ = 12th = 57

20, 20, 21, 24, 27, 29, 33, 33, 36, 39, 50, 57, 60, 65, 65

CONSTRUCT MEANING

Quartiles• Quartiles are more useful when comparing two sets of data.

• Here are the ages of another golf club. Calculate the median and quartiles and compare the ages of the members of the two golf clubs

• Lower Quartile: = = = 4.5th = 27• Median: = = = 9th = 47• Upper Quartile: 3 x LQ = 13.5th = 54

18, 23, 25, 27, 27, 37, 38, 45, 47, 49, 49, 50, 50, 58, 61, 66, 69

CONSTRUCT MEANING

Quartiles

Golf Club A Golf Club B

Lower Quartile 24 27Median 33 47Upper Quartile 57 54

• Which golf club has more younger members?

• Which golf club has more older members?

• What can you say about the age profile of each golf club in general?

DEMONSTATE UNDERSTANDING

Quartiles

• The Interquartile Range (IQR) is the upper quartile – the lower quartile

• It tells us how spread out the middle 50% of the data is

• Smaller IQR means more consistency and vice-versa

CONSTRUCT MEANING

QuartilesGolf Club A Golf Club B

Lower Quartile 24 27Median 33 47Upper Quartile 57 54

Golf Club A Golf Club B

Lower Quartile 24 27Median 33 47Upper Quartile 57 54Interquartile Range 33 27

“Members of golf club B are more similar in age than in golf club A”

CONSTRUCT MEANING

Box Plots

• A box plot is a way of illustrating key information about a set of data

• They are also very useful for comparing the distribution of two sets of data (e.g. boys vs girls)

CONSTRUCT MEANING

Box Plots

• To draw a box plot, you need FIVE pieces of information:

• The minimum value• The lower quartile• The median• The upper quartile• The maximum value

CONSTRUCT MEANING

Box Plots

CONSTRUCT MEANING

• Minimum Value: 3• Lower Quartile: 4• Median: 7• Upper Quartile: 9• Maximum Value: 10• Interquartile Range: 5

0 10987654321

The Interquartile Range (IQR) is the UQ – LQ.

It illustrates the spread of the middle 50% of the data.

The larger the IQR, the more spread out, and less consistent the data.

Maths Test Scores

• The box plot below shows the data for 23 female students.

0 10987654321

BOYS

0 10987654321

Maths Test Scores

GIRLS• Girls median higher

so on average, girls scored higher

• IQR lower so girls results were more consistent

• Girls minimum value was higher so boys scored the lowest

Golf Club A Golf Club B

Minimum Value 18 19Lower Quartile 24 27Median 33 47Upper Quartile 57 54Maximum Value 63 67

Box Plots

Draw box plots to represent the age of members of the two golf clubs

DEMONSTATE UNDERSTANDING

Box Plots• Below are the midday temperatures for Ringwood over the

past 11 days (in oC).

20, 22, 16, 17, 16, 18, 20, 18, 16, 21, 18

• Below are the midday temperatures for Glasgow over the past 11 days (in oC).

17, 20, 20, 17, 16, 14, 13, 19, 21, 17, 18

• Draw box plots for the data and write some comments on what they tell you about the temperatures in Ringwood and Glasgow over the past 11 days.

REVIEW