Data Description
Lecture Number 3
October 19, 2016
Lecture Number 3
Data Description
October 19, 2016
1 / 51

Outline of Lecture 3
1
Introduction
2
Measures of Central Tendency
3
Measures of Variability
4
Chebyshev’s Theorem and The Empirical Rule
5
Skewness
6
Distribution Shapes
7
Measures of Position
8
Exploratory Data Analysis(EDA)
Lecture Number 3
Data Description
October 19, 2016
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Introduction
There are three (3) major characteristics of a single variable that we
tend to look at:
(1)
Central tendency;
(2)
Variability or Dispersion; and
(3)
Distribution.
These three can help us make some statistical summary statements
about a large and complex set of individual values for a variable
Graphs can help you describe the basic shape of a data distribution;
”a picture is worth a thousand words.”
There are limitations, however, to the use of graphs - e.g. graphs are
somewhat imprecise for use in statistical inference.
One way to overcome limitations of graphs is to use
numerical
measures
, which can be calculated for either a sample or a
population of measurements.
You can use the data to calculate a set of numbers that will convey a
good mental picture of the frequency distribution.
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October 19, 2016
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Measures of Central Tendency
Definition of measures of central tendency
A measure of central tendency is a single value that attempts to describe a
set of data by identifying the central position within that set of data. As
such, measures of central tendency are sometimes called measures of
central location.
Thus, the purpose of measures of central tendency is to identify the
location of the centre of a given distribution.
There are generally three measures of central tendency:
the mean;
the median; and the mode.
Note that: measures found by using all the data values in the
population are called
parameters
while those calculated by using the
data values from samples are called
statistics
!
Secondly, it is important to note that one needs to know how to
calculate these measures for both ungrouped and grouped data!
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October 19, 2016
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Measures of Central Tendecny - The Mean
Definition of Mean
The mean is defined as the arithmetic average of a set of data values
(measurements or observations), that is, the sum of the values divided by
the total number of values.
It is a very common and useful measure of center and is often referred
to as the arithmetic mean, or simply the average, of a set of
measurements.
To distinguish between the mean for the sample and the mean for the
population, we will use the symbol ¯
x
read as: ”x-bar” for a sample
mean and the symbol
μ
(Greek lower case mu) for the mean of a
population.
Since most statistical formulas (including one for the mean) involve
adding or ”summing” numbers, we use a shorthand symbol ,
∑
(Greek capital sigma),to indicate the process of summing.

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