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Cumulative Frequency and Box Plots. Learning Objectives. To be able to draw a cumulative frequency curve and use it to estimate the median and interquartile range and draw a box plot. Does anybody remember how to draw a Cumulative Frequency Diagram?. Cumulative Frequency Curves

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learning objectives
Learning Objectives
  • To be able to draw a cumulative frequency curve and use it to estimate the median and interquartile range and draw a box plot
slide4
Cumulative Frequency Curves
  • Cumulative Frequency = a running total of the data
  • Median = Half way up the Cumulative Frequency
  • Lower Quartile(LQ) = ¼ way up Cum Freq
  • Upper Quartile (UQ) = ¾ way up Cum Freq
  • Inter Quartile Range = UQ - LQ
big worked example
Big Worked Example

The table below shows the number of minutes students were late for their fun algebra lesson.

(a) Draw a Cumulative Frequency Diagram of the data

(b) Use it to find the Median, Lower Quartile, Upper Quartile, and Inter Quartile Range

(c) Draw a Box-Plot assuming a minimum time of o minutes and a maximum of 25 minutes

slide6

x

80

x

Cum freq

60

x

Median = Middle Value

40

  • QUARTILES
  • Lower Quartile = ¼ way
  • Upper Quartile = ¾ way

x

20

x

12½

15½

5

10

15

20

25

t mins

Interquartile Range

= 15½ - 8½ = 7 mins

slide8

1

2

5

3

4

Box Plots

  • Box Plots (Box and Whisker Diagram) are another way of displaying data for comparison
  • To draw a Box Plot we need FIVE pieces of information:
    • 1. The Minimum Value
    • 2. Lower Quartile (Q1)
    • 3. The Median (Q2)
    • 4. Upper Quartile (Q3)
    • 5. Maximum Value
  • They are drawn in the following way:
  • BOX = The location of the middle 50% of the data
  • WHISKERS = How the data is spread overall
slide9

70

60

50

¾

40

Cumulative Frequency

½

IQR = 38 – 21 = 17 mins

30

20

¼

Median = 27

10

UQ = 38

LQ = 21

0

40

50

20

30

60

70

10

Minutes Late

20

0

10

30

40

50

60

Box Plot from Cumulative Frequency Curve

box plot

Lower Quartile

Lowest value

Highest value

Median

Upper Quartile

0

5

10

15

20

25

t mins

Box Plot
slide11
Work
  • Ex 7:1
    • Page 62
    • Questions 5 and 6