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Cumulative Frequency
Diagrams & Box Plots
OCR Stage 8
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Cumulative Frequency
Time
t minutes0≤t! !≤t"0 "0≤t"! "!≤t#0 #0≤t#!
$um%er ostu'ents
"0 "( )0 ## #
CumulativeFrequency
10 26 56 78 80
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5 10 15 20 25 t mins
Cum freq
20
40
60
80
x
x
x
xx
Median = Middle Value
QUARTI!"*#$er Quar%ile = & $a'
*U((er Quar%ile = ) $a'
In%erquar%ile Ran*e
8+ 15+12+
= 15+ , 8+ = 7 min-
% minu%e- 0.%/5 5.%/10 10.%/15 15.%/20 20.%/25
C 10 26 56 78 80
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Box Plot
5 10 15 20 25 t mins0
+o,est value -ig.est value/e'ian
+o,er uartile122er uartile
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C u m &
r e
q
Com2aring # sets o 'ata
Median = 62*
#$er Quar%ile = 52*
U((er Quar%ile = 70*
In%erquar%ile ran*e
= 70 52 = 18*
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C u m &
r e q
Com2aring # sets o 'ata
Median = 78*
#$er Quar%ile = 66*
U((er Quar%ile = 83*
In%erquar%ile ran*e
= 83 66 = 2*
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Box Plots
40 60 80 100 120 m kg 20
IQR-18
2M!IA" 78 and 62
9"
:IR"
Median = 78*
#$er Quar%ile = 66*
;i*
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Com2arison statements
* Boys .ave a larger /3D45$ so
6 on average7 t.ey are .eavier t.an girls
6 t.e average %oy is "(g .eavier t.an t.e
average girl
* Boys .ave larger 4nterquartile Range so
6 %oys9 ,eig.ts vary more t.an girls9 ,eig.ts
* :.y 'o ,e $OT use t.e Range;
6 One extreme value can 'istort t.e com2arison