HISTOGRAMS Representing Data Module S1
Mar 28, 2015
Why use a Histogram
When there is a lot of data When data is
Continuous a mass, height, volume, time etc
Presented in a Grouped Frequency Distribution usually in groups or classes that are UNEQUAL
AREA is proportional to FREQUENCY
NOT height, because of UNEQUAL classes!
So we use FREQUENCY DENSITY = Frequency Class width
Grouped Frequency Distribution
Time taken (nearest minute)
5-9 10-19 20-29 30-39 40-59
Freq 14 9 18 3 5
Speed, kph 0< v ≤40 40< v ≤50 50< v ≤60 60< v ≤90 90< v ≤110
Frequency 80 15 25 90 30
ClassesNo gaps
GAPS! Need to adjust to Continuous
Ready to graph
Adjusting Classes
Class Widths
Time taken (nearest minute)
5-9 10-19 20-29 30-39 40-59
Freq 14 9 18 3 5
9½4½ 19½ 29½ 39½ 59½
105 10 10 20
Frequency Density
Time taken (nearest minute) 5-9 10-19 20-29 30-39 40-59
Freq 14 9 18 3 5
Class width 5 10 10 10 20
Frequency Density 2.8 0.9 1.8 0.3 0.25
Drawing
Sensible Scales Bases correctly aligned
Plot the Class Boundaries Heights correct
Frequency Density
Estimating a Frequency
Imagine we want to Estimate the number of people with a time between 12 and 25 mins
Because rounded to nearest minute Consider the interval 11.5 to 25.5
4.5 19.59.5 29.5 39.5 49.5 59.5
3.0
2.0
1.0
Fre
q D
en
s
Time (Mins)
11.5 25.5
Frequency = 0.9 x 8 = 7.2
Frequency = 1.8 x 6 = 10.8
Total Frequency = 18
…and the other one?
Simpler to plot No adjustments required – class widths friendly No ½ values
Estimation from the EXACT values given No adjustment required Estimate 15 to 56 would use 15 and 56!
Appear LESS OFTEN in the exam
Speed, kph 0< v ≤40 40< v ≤50 50< v ≤60 60< v ≤90 90< v ≤110
Frequency 80 15 25 90 30