Chapter 2Frequency Distribution

2.1Discrete & Continuous Variable

Variable - a characteristic of a population varies from one to one

e.g.x : the height of s.3 students, x may be 167cm, 170cm...

Qualitative variable - not numerical values e.g. sex, colour...

Quantitative variable - numerical values

discrete variable - only isolated values

continuous variable - theoretically any value in a interval

2.2Frequency Table

Frequency table for discrete data / Frequency table for continuous data
Brothers / f / marks / f
3 / 2 / 51-55 / 2
7 / 3 / 56-60 / 3
.
. / .
.

Procedure of constructing frequency tables

1.Recognize the precision P. 61
2.Find the largest and the smallest values
3.Divide into non-overlapping class
3.15 - 20 classes, preferably no empty class
3.2If possible, class width equal
3.3Specify class by class limits51 - 55
56 - 60
or class boundaries50.5 - 55.5
55.5 - 60.5
or intervals 51  x < 56
56  x < 61
61 x < 66
4.If necessary, find class marks
5.Find the class frequency and if necessary relative frequency
- for continuous distribution, find also cumulative frequency

2.3Graphical Representation

Bar Charts - for discrete variable

- width insignificant

- height  frequency or data to be shown

Histogram- for continuous variable

-if width equal,height  frequency 

 area  frequency

if width unequal, height  frequency density 

(frequency/class width)

Frequency Polygon - joining the mid-point of the top of each bar in the histogram

- can be smoothed to become Frequency Curve

- give me a overall picture of the distribution

Symmetric

positively skewed(right-skewed)/ negatively skewed(left-skewed)

Cumulative Frequency - plotted upper class boundaries against cumulative frequency

Polygon

Stem-and-leaf Diagram - leaf may be truncated to made it more easy be read

- advantages1.easy to construct

2.partly a table & partly a graph

3.retains information

4.ready for finding quartiles

- disadvantages1.stems are very small or large  unable to show distribution

  1. not suitable for large set of data  unable to show distribution

2.4Statistical Measures for Frequency Distribution

Discrete Frequency Distribution

PopulationSample

fi xi

Continuous Frequency Distribution

-use class marks replace raw data

- Quartiles From Histogram pth q-tiles = xm-1 + (xm-xm-1)

 

how many data has to  class width

be count in this class

From C. F. Polygon/Curve : read the value

From Stem-and-leaf diagram (Before grouped into intervals)

read the corresponding data from the diagram

- Symmetry Vs skewness

right-skewedmode < median < meanleft-skewed mean < median < mode

symmetrical distribution

mean = median = mode

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