Dr. Prabath KarunanayakeMBBS, MBA in HRM, PGDipPsych, PGDipOHSFormer Head of HR, Access Engineering PLC

10th November 2013

Analysis and Presentation of Data

Statistics

Things aren’t always what we think!

Six blind men go to observe an elephant.

One feels the side and thinks the elephant is like a wall. One feels the tusk and thinks the elephant is a like a spear. One touches the squirming trunk and thinks the elephant is like a snake. One feels the knee and thinks the elephant is like a tree. One touches the ear, and thinks the elephant is like a fan. One grasps the tail and thinks it is like a rope. They argue long and loud and though each was partly in the right, all were in the wrong.

1 2 3 4 5 60

20

40

60

80

100

120

1 2 3 4 5 689

91

93

95

97

99

101

103

105

WHAT IS STATISTICS ?

Statistics is the branch

of mathematics

concerned with

collecting, organizing,

analyzing and drawing

conclusions from

numerical data

To be able to read and understand the various statistical studies performed in your field of study

To be able to conduct research in your field, for which statistical procedures are a basic requirement

To become better consumers and citizens by using the knowledge gained from studying statistics

WHY STUDY STATISTICS ?

BRANCHES OF STATISTICS

Inferential statisticsBranch of statistics that uses

data from samples to make predictions about the

population from which the sample is drawn

Descriptive statisticsBranch of statistics that provide a means of summarizing data

Descriptive Statistics

• Organize• Summarize• Simplify• Presentation of

data

Inferential Statistics • Generalize from

samples to pops• Hypothesis

testing• Relationships

among variables

Describing data Make predictions

3 Types

Frequency Distributions

Summary Statistics

Graphical Representations

# of observations that fall in a particular

category

Describe data in just one number

Tables and Graphs

DESCRIPTIVE STATISTICS

Frequency distributiontable An arrangement of scores from a sample that Indicates how often a particular score is present

HistogramGraphical representation Of the data where scores Are ordered in one axis and the number of observations are ordered in the other axis

Frequency polygon Line connecting the mid points of the tops of the rectangles in the histogram

FREQUENCY DISTRIBUTIONS Class Class Frequency Cumulative limits boundaries frequency

100 - 104 105 - 109110 - 114115 - 119120 - 124125 - 129130 - 134

28

1813711

2102841484950

99.5 - 104.5104.5 - 109.5109.5 - 114.5114.5 - 119.5119.5 - 124.5124.5 - 129.5129.5 - 134.5

3 types

Central Tendency

Dispersion

Central location within a distribution of scores

Spread or variability of scores in a distribution of

scores

Position

Relative position of a data value in a data set

SUMMARY STATISTICS

An index of the central location within a distribution of scores; the most representative score in a distribution of scores

Mean

The average of all scores, arrived by adding scores together and dividing by the number of scores

Median

The point in a distribution of scores that divide the distribution exactly in half when the scores are listed in numerical order

Mode

The most frequently occurring score in a set of scores

CENTRAL TENDENCY

An index of the spread or variability of scores in a distribution of scores

Range

The difference between the highest and lowest score in a distribution

Standard deviation

The average deviation of a set of scores from the center of the distribution

DISPERSION

DISTRIBUTION CURVES

An index of the relative position of a data value in a data set

Standard score

Number of standard deviations that a given value is below or above the mean

Percentiles, deciles and quartiles

Describing the position of a data value by dividing the data range into equal groups

- find the percentile for a given value

- find the value for a given percentile

POSITION

TABULAR REPRESENTATIONSA method of data presentation that help to make a further study on the properties of the data distribution.

Frequency Distribution Table

Relative Frequency DistributionA table in which frequency is presented as the ratio to the total frequency.

Cumulative Frequency DistributionA table in which the cumulative value of each subsequent class is presented.

Cross TabulationCategorize data on the basis of more that one variable at the same time.

GRAPHICAL REPRESENTATIONS