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Frequency Polygons Histograms Positive Skew Negative Skew Block 2 Revision Stem and Leaf Diagrams Comparative Pie Charts Two Way Table Stem and Leaf Diagrams This is a good Stem and Leaf Diagram : 1 6 6 7 8 8 2 1 2 4 5 5 6 7 9 3 5 5 7 7 7 8 4 0 0 1 2 Box masses Key: 3 7 = 3.7 kg

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block 2 revision

Frequency Polygons

Histograms

Positive Skew

Negative Skew

Block 2 Revision

Stem and Leaf Diagrams

Comparative Pie Charts

Two Way Table

stem and leaf diagrams
Stem and Leaf Diagrams

This is a good Stem and Leaf Diagram:

1 6 6 7 8 8

2 1 2 4 5 5 6 7 9

3 5 5 7 7 7 8

4 0 0 1 2

Box masses

Key: 3 7 = 3.7 kg

stem and leaf diagrams3
Stem and Leaf Diagrams

Male

Female

  • FEATURES
  • One ‘stem’, two ‘branches’
  • ‘Leaves’ increase in size from the ‘stem’ outwards
  • Compare two distributions

11 4

3 12 0 6

7 6 2 13 1 2 4 9

8 4 1 0 14 3 5 7

9 7 7 15 8

4 1 16 0

Key:

0 14 3

This represents 14 yrs 3 months.

stem and leaf diagrams4
Stem and Leaf Diagrams

Make sure when using a Stem and Leaf Diagram you have:

  • A title to show what the Stem and Leaf Diagram shows.
  • A key so that you can tell how the Stem and Leaf diagram is working.
  • Align all the numbers in rows so that it is easier to see.
  • Each row in numerical order.
comparative pie charts
Comparative Pie Charts
  • On a pie chart, frequency is determined by SECTOR AREA and not just by ANGLE
  • On a single pie chart, the radius is constant, so the Angle is sufficient to determine the frequency
  • On two pie charts being compared, each “pie” area represents the entire frequency of one distribution
comparative pie charts6
Comparative Pie Charts

How do you compare two pie charts?

If a Pie Chart represents 50 people. It has a radius 2 cm.

Area = p x r x r = 4 p

And a Pie Chart represents ??? people. It has a radius of 4 cm.

Area = p x r x r = 16 p

This is 4 times the area of the 1st Pie Chart.

So it represents 4 x 50 = 200 people.

comparative pie charts7
Comparative Pie Charts

How do you compare two pie charts?

Pie Chart 1 represents 40 acres. It has a radius of 3 cm.

I need Pie Chart 2 to represent 1000 acres. It has radius r cm.

Write as a ratio the two frequencies:

40 : 1000 = 4 : 100

Square root:

2 : 10 = 1 : 5

This means that the second radius is 5 x the first i.e. r = 15 cm

frequency polygons
Frequency Polygons

Frequency

Length (mm)

30

35

40

45

50

55

60

65

frequency polygons11
Frequency Polygons

Frequency

Length (mm)

30

35

40

45

50

55

60

65

histograms
Histograms

Make sure you don’t:

  • Under-Simplification (not simplified enough)
  • Over-Simplification (simplified too much)

Choose the group width carefully.

Make it too small (under-simplification) and get too many bars.

Make it too big (over-simplification) and get too few bars.

Get it just right and your graph will tell a story

positive skew
Positive Skew

One end has been stretched to the right.

The mean is more than the median.

negative skew
Negative Skew

One end has been stretched to the left.

The mean is less than the median.