Cumulative Frequency and Box Plots
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Transcript of Cumulative Frequency and Box Plots
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Cumulative Frequency and Box
Plots
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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
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Does anybody remember how to draw a Cumulative Frequency Diagram?
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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
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Big Worked ExampleThe 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) Number of Students
Cumulative Frequency
0 < t ≤ 5 105 < t ≤ 10 16
10 < t ≤ 15 3015 < t ≤ 20 2220 < t ≤ 25 2
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5 10 15 20 25 t mins
Cum freq
20
40
60
80
x
x
x
x x
Median = Middle Value
QUARTILES• Lower Quartile = ¼ way• Upper Quartile = ¾ way
Interquartile Range
8½ 15½12½
= 15½ - 8½ = 7 mins
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Does anybody have any idea what a Box Plot is?
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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
3 41
2 5
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10
20
30
40
50
60
70
0
Cum
ulat
ive
Freq
uenc
y
10 20 30 40 50 60 70Minutes Late
Med
ian
= 27LQ
=
21 UQ =
38
IQR = 38 – 21 = 17
mins
½
¼
¾
0 10 20 30 40 50 60
Box Plot from Cumulative Frequency Curve
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Box Plot
5 10 15 20 25 t mins0
Lowest value
Upper Quartile
Highest value
Lower Quartile
Median
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Work• Ex 7:1
– Page 62– Questions 5 and 6