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 ...
Does anybody remember how to draw a
Cumulative Frequency Diagram?
Cumulative Frequency Curves
•

Cumulative Frequency = a running total of the data

•

Median = Half way up the Cumulative ...
Big Worked Example
The table below shows the number of minutes students were late
for their fun algebra lesson.
(a) Draw a...
80

x

x

Cum freq

60

x
Median = Middle Value

40

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

x
20
x

5
...
Does anybody have any idea what a Box
Plot is?
Box Plots
•

Box Plots (Box and Whisker Diagram) are another way of displaying
data for comparison

•

To draw a Box Plot ...
Box Plot from Cumulative Frequency Curve
70

50

¾

40

¼

10
0

10

20

30

UQ = 38

20

IQR = 38 – 21
= 17 mins
Median =...
Box Plot
Lowest value

Lower Quartile

0

Highest value

Median

5

10

Upper Quartile

15

20

25

t mins
Work
• Ex 7:1
– Page 62
– Questions 5 and 6
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Cumulative freqeuncy and_box_plots

  1. 1. Cumulative Frequency and Box Plots
  2. 2. 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
  3. 3. Does anybody remember how to draw a Cumulative Frequency Diagram?
  4. 4. 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
  5. 5. 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 Time t (mins) 0<t≤5 5 < t ≤ 10 10 < t ≤ 15 Number of Students 10 16 30 15 < t ≤ 20 22 20 < t ≤ 25 2 Cumulative Frequency
  6. 6. 80 x x Cum freq 60 x Median = Middle Value 40 QUARTILES •Lower Quartile = ¼ way •Upper Quartile = ¾ way x 20 x 5 8½ 10 Interquartile Range 12½ 15½ 15 20 = 15½ - 8½ = 7 mins 25 t mins
  7. 7. Does anybody have any idea what a Box Plot is?
  8. 8. 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. 2. 3. 4. 5. The Minimum Value Lower Quartile (Q1) The Median (Q2) Upper Quartile (Q3) Maximum Value They are drawn in the following way: 1 2 3 4 5
  9. 9. Box Plot from Cumulative Frequency Curve 70 50 ¾ 40 ¼ 10 0 10 20 30 UQ = 38 20 IQR = 38 – 21 = 17 mins Median = 27 30 ½ LQ = 21 Cumulative Frequency 60 40 50 60 70 Minutes Late 0 10 20 30 40 50 60
  10. 10. Box Plot Lowest value Lower Quartile 0 Highest value Median 5 10 Upper Quartile 15 20 25 t mins
  11. 11. Work • Ex 7:1 – Page 62 – Questions 5 and 6

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