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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