cumulative frequency
DESCRIPTION
Cumulative Frequency. How to draw a cumulative frequency graph. If the data is jumbled, sort it out by using a table. 23, 24, 34, 45, 56, 23, 57, 41, 37, 65, 17, 26, 35, 44, 33, 48, 19, 61, 58, 55, 49, 44, 57, 43. You must decide sensible intervals. - PowerPoint PPT PresentationTRANSCRIPT
Cumulative Frequency
How to draw a cumulative frequency
graph
If the data is jumbled, sort it out by using a table
23, 24, 34, 45, 56, 23, 57, 41, 37, 65, 17, 26, 35, 44, 33, 48, 19, 61, 58, 55, 49, 44, 57, 43
Data Frequency
10 – 20 2
20 – 30 4
30 – 40 5
40 – 50 7
50 – 60 4
60 – 70 2
You must decide sensible intervals
Complete the third column by adding the second column like this:
Data Frequency Cumulative Frequency
10 – 20 2 2
20 – 30 4 2 + 4 = 6
30 – 40 5 2 + 4 + 5 = 11
40 – 50 7 2 + 4 + 5 +7 = 18
50 – 60 4 2 + 4 + 5 +7 + 4 = 22
60 – 70 2 2 + 4 + 5 +7 + 4 + 2 = 24
You don’t have to show workingData Frequency Cumulative
Frequency
10 – 20 2 2
20 – 30 4 6
30 – 40 5 11
40 – 50 7 18
50 – 60 4 22
60 – 70 2 24
Plot the second number in the data column against the number in the cumulative frequency column
Data Frequency Cumulative Frequency
10 – 20 2 2
20 – 30 4 6
30 – 40 5 11
40 – 50 7 18
50 – 60 4 22
60 – 70 2 240
5
10
15
20
25
30
0 10 20 30 40 50 60 70 80
Data
Cunu
lative
Frequ
ency Series1
Plot these numbers
Now, join up the points
0
5
10
15
20
25
30
0 10 20 30 40 50 60 70 80
Data
Cum
ulat
ive
Freq
uenc
y
Series1
You can use this to find the middle half
0
5
10
15
20
25
30
0 10 20 30 40 50 60 70 80
Series1
¾ (18)
½(12)
¼(6)
Lower Q(30)
Median(42)
Upper Q(53)
This means that the middle half is between 30 and 53. Called the
inter-quartile range.53 – 30 = 23
The Lower Quartile is 30
Median is 42
The Upper Quartile is 53
EXAMPLECUMULATIVE FREQUENCY GRAPHS
Cost frequency upper class boundarycumulative
freq
0 0 c < 0
0 c < 10 13 10 13 c < 10
10 c < 15 53 15 66 c < 10
15 c < 20 97 20 163 c < 20
20 c < 25 145 25 308 c < 25
25 c < 30 81 30 389 c < 30
30 c < 35 40 35 429 c < 35
35 c < 40 23 40 452 c < 40
40 c < 45 12 45 464 c < 45
45 c < 50 6 50 470 c < 50
CUMULATIVE FREQUENCY GRAPHS
c freq cost
0 c < 0
13 c < 10
66 c < 10
163 c < 20
308 c < 25
389 c < 30
429 c < 35
452 c < 40
464 c < 45
470 c < 50
470 / 2 = 235 this gives the median
1 / 4 x 470 = 117.5 this gives lower quartile
3 / 4 x 470 = 352.5 this gives the upper quartile
Cumulative Frequency Graph
-400
-300
-200
-100
0
100
200
300
400
500
0 10 20 30 40 50 60
Cost
Cu
mu
lati
ve
fre
qu
en
cy
c freq cost
0 c < 0
13 c < 10
66 c < 10
163 c < 20
308 c < 25
389 c < 30
429 c < 35
452 c < 40
464 c < 45
470 c < 50
BIG graph – a whole sheet of graph paper
Cumulative Frequency Graph
-400
-300
-200
-100
0
100
200
300
400
500
0 10 20 30 40 50 60
Cost
Cu
mu
lati
ve
fre
qu
en
cy
c freq cost
0 c < 0
13 c < 10
66 c < 10
163 c < 20
308 c < 25
389 c < 30
429 c < 35
452 c < 40
464 c < 45
470 c < 50
Q2 1 /2 x 470 = 235th value this gives the median which is about £22.50
Q1 1 / 4 x 470 = 117.5th value this gives lower quartile Q1 which is about £17.70
Q3 3 / 4 x 470 = 352.5th value this gives the upper quartile Q3 which is about £27.70
BIG graph – a whole sheet of graph paper
Cumulative Frequency Graph
-400
-300
-200
-100
0
100
200
300
400
500
0 10 20 30 40 50 60
Cost
Cu
mu
lati
ve
fre
qu
en
cy
Whiskers to highest and lowest values
Q1 Q2 Q3