EDUCATIONAL STATISTICS_Unit_I.ppt

EDUCATIONAL STATISTICS
UNIT-I
DESCRIPTIVE STATISTICS –
QUANTITATIVE DATA
Dr.N.SASIKUMAR
Assistant Professor
Department of Education
Alagappa University
Karaikudi-630003

DESCRIPTIVE STATISTICS
Descriptive statistics summarizes or
describes characteristics of a data set.
Descriptive statistics consists of two basic
categories of measures: measures of central
tendency and measures of variability (or
spread).
Measures of central tendency describe the
center of a data set.
Measures of variability or spread describe
the dispersion of data within the set.

 Descriptive statistics, in short, help describe and understand
the features of a specific data set by giving short summaries
about the sample and measures of the data.
 The most recognized types of descriptive statistics are
measures of center: the mean, median and mode, which are
used at almost all levels of math and statistics. The mean, or
the average, is calculated by adding all the figures within the
data set and then dividing by the number of figures within the
set.
 For example, the sum of the following data set is 20: (2, 3, 4,
5, 6). The mean is 4 (20/5). The mode of a data set is the
value appearing most often, and the median is the figure
situated in the middle of the data set. It is the figure
separating the higher figures from the lower figures within a
data set. However, there are less common types of descriptive
statistics that are still very important.

SCALE OF MEASUREMENT
 In Statistics, the variables or numbers are defined and
categorized using different scales of measurements. Each
level of measurement scale has specific properties that
determine the various use of statistical analysis.
 Levels of Measurements
There are four different scales of measurement. The data
can be defined as being one of the four scales. The four
types of scales are:
 Nominal Scale
 Ordinal Scale
 Interval Scale
 Ratio Scale


NOMINAL SCALE
 Nominal scales are used for labeling variables, without any
quantitative value. “Nominal” scales could simply be called “labels.”
 Here are some examples, below. Notice that all of these scales are
mutually exclusive (no overlap) and none of them have any numerical
significance. A good way to remember all of this is that “nominal”
sounds a lot like “name” and nominal scales are kind of like “names”
or labels.
 Examples of Nominal Scales

ORDINAL SCALE
 The order of the values is what’s important and significant, but the differences
between each one is not really known. Take a look at the example below. In
each case, we know that a #4 is better than a #3 or #2, but we don’t know–and
cannot quantify–how much better it is. For example, is the difference between
“OK” and “Unhappy” the same as the difference between “Very Happy” and
“Happy?” We can’t say.
 Ordinal scales are typically measures of non-numeric concepts like
satisfaction, happiness, discomfort, etc.
 “Ordinal” is easy to remember because is sounds like “order” and that’s the
key to remember with “ordinal scales”–it is the order that matters, but that’s
all you really get from these.

INTERVAL SCALE
 Interval scales are numeric scales in which we know both the
order and the exact differences between the values. The classic
example of an interval scale is Celsius temperature because the
difference between each value is the same. For example, the
difference between 60 and 50 degrees is a measurable 10
degrees, as is the difference between 80 and 70 degrees.
 Interval scales are nice because the realm of statistical analysis
on these data sets opens up. For example, central tendency can
be measured by mode, median, or mean; standard deviation can
also be calculated.
 Like the others, you can remember the key points of an
“interval scale” pretty easily. “Interval” itself means “space in
between,” which is the important thing to remember–interval
scales not only tell us about order, but also about the value
between each item

Characteristics of Interval Scale
 The interval scale is quantitative as it can quantify the difference
between the values
 It allows calculating the mean and median of the variables
 To understand the difference between the variables, you can subtract
the values between the variables
 The interval scale is the preferred scale in Statistics as it helps to assign
any numerical values to arbitrary assessment such as feelings, calendar
types, etc.

RATIO SCALE
 Ratio scales have all of the characteristics of interval scales
as well as a true zero, which refers to complete absence of
the characteristic being measured.
 Physical characteristics of persons and objects can be
measured with ratio scales, and, thus, height and weight
are examples of ratio measurement.
 A score of 0 means there is complete absence of height or
weight. A person who is 1.2 metres (4 feet) tall is two-
thirds as tall as a 1.8-metre- (6-foot-) tall person. Similarly,
a person weighing 45.4 kg (100 pounds) is two-thirds as
heavy as a person who weighs 68 kg (150 pounds).

Nominal variables are used to “name,” or
label a series of values.
Ordinal scales provide good information
about the order of choices, such as in a
customer satisfaction survey.
Interval scales give us the order of values +
the ability to quantify the difference
between each one.
Finally, Ratio scales give us the ultimate–
order, interval values, plus the ability to
calculate ratios since a “true zero” can be
defined.

Summary of data types and scale measures

3
Introduction
A graphical representation is a visual
display of data and statistical results. It is
more often and effective than presenting
data in tabular form.
 There are different types of graphical
representation and which is used depends
on the nature of the data and the nature
of the statistical result.
ORGANIZATION AND GRAPHICAL
PRESENTATIONOF DATA

PURPOSE
 Compare categorical data
Compare series of data over time
 Percentage of totalcomparisons
 Relationship between two variables
Relationship between three variables
4

Typesof Graphical Presentation
There are many types of Graphical
presentation-
 Circle or Pie Diagram
 Bar Diagram
 Comparative Bar Diagram
 Histogram
 Frequency polygon
 Cumulative frequency cure or Ogive
5

Circle or Pie Diagram
A pie chart displays data as a percentage of the
whole. Each pie section should have a label and
percentage. A total data number should be
included.
6
Pie Diagram
No. of Students in Each
Subject
Science , 500,
32%
Arts, 300,
19%
English ,
450,
28%
Medicine ,
100,
6%
Commerces ,
150, 9%
Maths , 100,
6%
Science
Arts
English
Maths
Commerce
s Medicine

Advantages 7
 Visually appealing
 Summarize a large data set in visual form
 Be visually simpler than other types of graph
 Shows percent of total for each category
Disadvantages
 No exact numerical data
 Hard to compare 2 data sets
 Total unknown unless specified
 Use only with discrete data

Bar Diagram
 Bar graph are commonly used to show
the number or proportion of nominal or
ordinal data which possess a particular
attribute. They depict the frequency of
each category of data point as a bar
rising vertically from the horizontal
axis.
8

Bar Diagram 9
Division
Percentage
(%)
I 20
II 30
III 30
fail 15
Result
Awaited
5

Advantages 1
0
 Visually strong.
 Bar graph displays discrete data in separate columns.
 Estimate key values at a glance.
 summarize a large data set in visual form
 Permit a visual check of the accuracy.
Disadvantages
 Graph categories can be reordered to emphasize
certain effects.
 Require additional written or verbal explanation.
 Be easily manipulated to yield false impressions
 Be inadequate to describe the attribute, behavior
.

Comparative Bar Graph
1
1
 A graph using parallel bars of varying
lengths, as to illustrate
comparative costs, exports, birth-rates,
etc.
Advantages
Can easily compare two or three data
sets.

Comparative Bar Graph
1
2
Divisio
n
Boys Girls
I 20 30
II 30 35
III 30 20
Fail 15 10
Others 5 5

Histogram Graph
A histogram displays continuous data
in ordered columns. Categories are of
continuous measure such as time,
inches, temperature, etc.

Advantages 1
5
 Visually strong
 Can compare to normal curve
 Usually vertical axis is a frequency count of items falling
into
each category
Disadvantages
 Cannot read exact values because data is grouped into
categories
 More difficult to compare two data sets
 Use only with continuous data

Frequency Polygon
 A frequency polygon can be made from a
line graph by shading in the area
beneath the graph. It can be made from
a histogram by joining midpoints of
each column.
1
6

Frequency Polygon
CI F
4-5 5
6-7 4
89 3
1
7

Advantages
 Visually appealing
1
8
Disadvantages
Anchors at both ends may imply zero
as data points.
Use only with continuous data.

Cumulative frequency Polygon
 A cumulative frequency distribution
(ogive) is used to determine how many
or what proportion of the data values
are below or above a certain value.
1
9

2
0
Cumulative Frequency Polygon

A diagram must be attractive, well
proportioned, neat and pleasing to the
eyes.
Graphical forms makes it possible to
easily draw visual impression of data.
Graphical presentation of data
enhances our understandings.
It makes comparisons easily.
This kind of method create an imprint
on mind for long period of time.
They should be geometrically accurate.

Descriptive Analysis
Measures of Central
Tendency
Measures of
dispersion/Variability
Measures of
Association
• Mean
• Median
• Mode
• Range
• Mean Deviation
• Quartile Deviation
• Standard Deviation
• Correlation
• Regression

Measures of Central Tendency
 Measures of central tendency are also usually called as the
averages. They give us an idea about the concentration of the
values in the central part of the distribution.
 The Mean, Median and Mode are the three measures of
central tendency.
 Mean is the arithmetic average of a data set. This is found by
adding the numbers in a data set and dividing by the number
of observations in the data set.
 The median is the middle number in a data set when the
numbers are listed in either ascending or descending order.
 The mode is the value that occurs the most often in a data set
and the range is the difference between the highest and
lowest values in a data set.

EDUCATIONAL STATISTICS_Unit_I.ppt

EDUCATIONAL STATISTICS_Unit_I.ppt

More Related Content

Similar to EDUCATIONAL STATISTICS_Unit_I.ppt (20)

More from Sasi Kumar (20)

Recently uploaded (20)

EDUCATIONAL STATISTICS_Unit_I.ppt