Demonstrate knowledge of measures and displays used to compare data sets

Displays bivariate data (data with two variables) so it can be compared

e.g. Draw a composite bar chart for this set of data, which gives information about the amount of elements (g) in 1 kg of three different types of fats.

Aluminium Carbon Iron

Saturated fat 24 18 26

Polyunsaturated fat

18 16 20

Monounsaturated fat

26 20 26

Total columns to work out height of axis/bars

68 54 72

Elements go on bottom axis

10

20

30

40

50

60

70

80

Element content in fat

Mas

s of

ele

men

t (g)

Aluminium Carbon Iron

Draw bars for saturated fats

Bars for polyunsaturated fats is placed on top etc

42 34 46

Add a keySaturated fatPolyunsaturated fatMonounsaturated fat

1. Mean

- easy to calculate but is affected by extreme values

- to calculate use:Sum of all valuesSum of all values

Total number of valuesTotal number of values

e.g. Calculate the mean of 6, 11, 3, 14, 8

6 + 11 + 3 + 14 + 8

5Mean = =

42

5

Push equals on calculator BEFORE dividing

= 8.4

– records and organises data– most significant figures form the stem and the final digits the leaves– can be in back to back form in order to compare two sets of data

e.g. Place the following heights (in m) onto a back to back stem and leaf plot BOYS = 1. 59, 1.69, 1.47, 1.43, 1.82, 1.70, 1.73, 1.35, 1.76, 1.68, 1.62, 1.84, 1.45, 1.50, 1.54, 1.73, 1.84, 1.71, 1.66  GIRLS = 1. 44, 1.46, 1.63, 1.29, 1.48, 1.57, 1.51, 1.42, 1.34, 1.45, 1.57, 1.59, 1.42

Unordered Graph of Heights Ordered Graph of Heights Boys Girls Boys Girls  1.8 1.8

1.7 1.7 1.6 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2

Place the final digits of the data on the graph on the correct side

,7

,9,9

,3

,2,0,3

5

,6,8,2

4

5,0 4

,3 1 6

,4

4, 6,

3

9

8,7, 1,

2,4

5,7, 9

2

4, 4, 26, 3, 3, 1, 0

9, 8, 6, 2 9, 4, 07, 5, 3

5

3 1, 7, 7, 92, 2, 4, 5, 6, 8

4 9

Graph of Heights Boys Girls  1.8 1.7

1.6 1.5 1.4 1.3 1.2

4, 4, 26, 3, 3, 1, 0

9, 8, 6, 2 9, 4, 07, 5, 3

5

3 1, 7, 7, 92, 2, 4, 5, 6, 8

4 9

e.g. From the ordered plot state the minimum, maximum, LQ, median, UQ, IQR and range statistics for each side

BOYS GIRLS

Minimum:Maximum:LQ:Median:UQ:IQR:Range:

For each statistic, make sure to write down the whole number, not just the ‘leaf’!

1.29 m1.63 m

1.63 – 1.29 = 0.34 m

When finding median, LQ and UQ, make sure you count/cross in the right direction!

LQ/UQ = 6 + 1 = 3.5 2

1.42 m1.46 m1.57 m

1.57 – 1.42 = 0.15 m

Remember: If you find it hard to calculate stats off graph, write out data in a line first!

1.35 m1.84 m1.50 m1.68 m1.73 m

1.73 – 1.50 = 0.23 m1.84 – 1.35 = 0.49 m

Median = 13 + 1 = 7 2

To find placement of median and LQ/UQ use: n + 1 2

– shows the minimum, maximum, LQ, median and UQ– ideal for comparing two sets of data

1.20 1.30 1.40 1.50 1.60 1.70 1.80

Height (m)

1.90

Note: Use the minimum and maximum values to determine length of scale

Males

Females

Question: What is the comparison between the boy and girl heights?

ANSWER?

Minimum LQ Median UQ Maximum

EVIDENCE?

e.g. Using the height data from the Stem and Leaf diagrams, draw two box and whisker plots (Boys and Girls)

Box and Whisker Plots of Boys and Girls Heights