grouped data median press ctrl-a ©2009 – not to be sold/free to use stage 4 year 9
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Grouped DataGrouped DataMedianMedian
Press Ctrl-APress Ctrl-A©2009 – Not to be sold/Free to use
Stage 4 Stage 4 Year 9Year 9
Grouped Data
In grouped data:
Data classes must not overlap.
Intervals must be of equal size.
They are used for a large range of scores.
A class centre (cc) is calculated by averaging the end points.
3
Cumulative Frequency Histogram/Polygon
Histogram
0 1 2 3 4 5
5
10
15
2025
30
Polygonx f Cumulative
Frequencycf
0 2
1 7
2 9
3 6
4 5
5 2
2
9
18
24
29
31
cf
x
Ogive
4
Median
0 1 2 3 4 5
5
10
15
20
25
30
cf
x
%
100%
0%
50%
Median=2.1 for continuous dataMedian=2 for discrete data
5
Class
Grouped Data – The Median
0-4
5-9
10-14
15-19
20-24
25-29
30-34
35-40
Class Centre
cc2
7
12
17
22
27
32
37
Tally
f cf
23
1
4
3
4
2
1
2
2+35
5+16
6+410
10+313
13+417
17+21919+120
There are 20 scores.
Therefore the median is the 10th and 11th scores.10th = 17
11th = 22
Median =
17+222
= 19.5
Σf=
20
6
Grouped Data – The Median
cc2
7
12
17
22
27
32
37
f cf
23
1
4
3
4
2
1
2
5
6
10
13
17
1920
|
2|
7|
12|
17|
22|
27|
32|
37 cc
5-
10-
15-
20-
cf Cumulative Frequency HistogramCumulative Frequency Polygon‘Ogive’Median
Median (rounds up) = 22