frequency distribution & graph

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Frequency

Distribution &

Graph

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.

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.

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

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.

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.


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

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.


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

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

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

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

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.

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

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

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

Line Graphs Line graphs are typically used to show the change or trend in a variable over

time.

Bar Chart In bar chart the classes are reported on the horizontal axis and the class

frequencies on the vertical axis.

Pie Chart A circle is divided proportionally to the relative frequency and portions of

the circle are allocated for the different groups.

Any Question?

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frequency distribution & graph

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