frequency distribution & graph
TRANSCRIPT
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WELCOMETO OUR
PRESENTATION
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GROUP MEMBERSNAME ID NO
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Frequency
Distribution &
Graph
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FREQUENCY DISTRIBUTION
Frequency Distribution is a grouping of data into mutually exclusive categories showing the number of observations in each class.
The number of hours each student studied last week.
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SOME IMPORTANT TERMS Class Limit: The class limits are the lowest and the highest values that can
be included in the class.
Class Interval: The class interval is obtained by subtracting the lower limit of a class from the lower limit of the next class. The class intervals should be equal. It is denoted here by i.
Class Frequency: The number of observations in each class. It is denoted here by f.
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Class Midpoint: A point that divides a class into two equal parts. This is the average of the upper and lower class limits.
Find the midpoint of each interval, use the following formula:
Upper limit + lower limit 2
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Characteristic of Class
There should be between 5 and 20 classes.The classes must be continuous.The classes must be exhaustive. The classes must be mutually exclusive.The classes must be equal in width.
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Construction of Frequency Distribution
Example:Here is some Ungroup data on the minimum minutes spending for Reading Newspaper of 30 People.15, 23, 19, 15, 18, 23, 14, 20, 13, 20, 17, 12, 20, 13, 21, 18, 29, 17, 18, 10, 26, 15, 14, 17, 30, 23, 12, 27, 16, 24.
Step One: First arranging the data into ascending order. Then we get the data as:10, 12, 12, 13, 13, 14, 14, 15, 15, 15, 16,17, 17, 17,18, 18, 18, 19, 20, 20, 20, 21, 23, 23, 23,24, 26, 27, 29, 30.
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Construction of Frequency Distribution
Step Two: Decide on the number of classes using the formula 2k ≥ nWhere, k = Minimum number of classes n = Number of observationsThere are 30 observations so, n = 30. Therefore, k = 5
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A Guide Not A Dictator
Strictly speaking the 2k rule is a guide, not a rule. If the 2k rule suggests you need 6 classes, also consider using 5 or 7 classes but certainly not 3 or 9.
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Construction of Frequency Distribution
Step Three: Determine the class interval or width using the formula
i ≥ (H-L) / k
= (30-10)/5
= 4
Frequency Distribution Table
Class Interval Tally Frequency(f)10 up to 14 514 up to 18 IIII 918 up to 22 III 822 up to 26 IIII 426 up to 30 IIII 4
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Class Midpoint
Class Interval Class Midpoint Frequency, f
10 up to 14 12 5
14 up to 18 16 9
18 up to 22 20 8
22 up to 26 24 4
26 up to 30 28 4
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Relative Frequency Distribution
Relative frequency of a class is the frequency of that class divided by to total number of frequency. fRF
n
Class Interval Frequency, f Relative Frequency
10 up to 14 5 5/30=0.16
14 up to 18 9 9/30=0.30
18 up to 22 8 8/30=0.26
22 up to 26 4 4/30=0.13
26 up to 30 4 4/30=.013
Total 30
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Graphic Presentation Of A Frequency Distribution
Group Data
For Continuous data or quantitative variables:
The three commonly used graphic forms are HistogramsFrequency PolygonsCumulative Frequency
Curve.
Ungroup Data Line graphs Bar Chart Pie Chart
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HISTOGRAM A Histogram is a graph in which the class midpoints or limits are marked
on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are represented by the heights of the bars and the bars are drawn adjacent to each other.
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Frequency Polygons
A Frequency Polygon consists of line segments connecting the points formed by the class midpoint and the class frequency.
0
2
4
6
8
10
12 16 20 24 26
Class Midpoint
Freq
uenc
y
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Cumulative Frequency Distribution
A Cumulative Frequency Distribution is used to determine how many or what proportion of the data values are below or above a certain value.
Cumulative Frequency
More Than Method Less Than Method
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More Than Method
Less Than Method
Class Interval Lower Limit Frequency, f Cumulative Frequency
10 up to 14 10 5 30
14 up to 18 14 9 25
18 up to 22 18 8 16
22 up to 26 22 4 8
26up to 30 26 4 4
Class Interval Upper Limit Frequency, f Cumulative Frequency
10 up to 14 14 5 5
14 up to 18 18 9 14
18 up to 22 22 8 22
22 up to 26 26 4 26
26up to 30 30 4 30
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Line Graphs Line graphs are typically used to show the change or trend in a variable over
time.
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Bar Chart In bar chart the classes are reported on the horizontal axis and the class
frequencies on the vertical axis.
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Pie Chart A circle is divided proportionally to the relative frequency and portions of
the circle are allocated for the different groups.
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Any Question?
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ThankYou!!!