Descriptive Statistics - Measures of Central Tendency (Mean - Median - Mode) - Measures of Dispersion ( Normal Curve - Co-efficient of Variation )

1. Unit–5: Descriptive Statistics: Measures of Central Tendency
&
Unit–4: Descriptive Statistics: Measures of Dispersion
Course code 8614

2.  An average is a single value, which represents
the set of data as whole. Since the average
tends to lie in the center of distribution they
are also called measure of central tendency.
There are three methods of measuring the
center of any data.
 Arithmetic mean
 The Median
 The Mode

3.  It is defined as the sum of all the observations
divided by the number of observations. It is
denoted by X.
When to use Arithmetic Mean:
 We use arithmetic mean, when we are required
to study social, economic and commercial
problems like production, price, export and
import. It helps in getting average income,
average price, average production etc.

4.  5, 10, 12, 16, 8, 42, 25, 15, 10, 7
Solution:
5+10+12+16+8+42+25+15+10+7=150/10
Mean = 15

5.  Median is the middle most value of a set of data
when the data is arranged in order of magnitude. If
the number of observations is in odd form, then
median is the mid value and if the number of
observations is even form, then median is the average
of two middle values.
When we Apply Median:
 We apply median to the situations, when the direct
measurements of variables are not possible like
poverty, beauty and intelligence etc.

6.  Example: 12,15, 10, 20, 18, 25, 45, 30,
26
 We need to make order of the data
 10, 12, 15, 18, 20, 25, 26, 30, 45
 So Mean = 20

7.  The most frequent value that occurs in the set
of data is called mode. A set of data may have
more than one mode or no mode. When it has
one mode it is called uni-modal. When it has
two or three modes it is called bi-modal or tri-
modal respectively.
 Example:
 12, 24, 15, 18, 30, 48, 20, 24
 So Mode = 24

8.  Measures of central tendency estimate normal
or central value of a data set, while measures
of dispersion are important for describing the
spread of the data, or its variation around a
central value.

9.  A measure of dispersion indicates the scattering of
data. In other words, dispersion is the extent to
which values in a distribution differ from the average
of the distribution. It gives us an idea about the extent
to which individual items vary from one another, and
from the central value.

10.  Measure # 1. Range:
 Measure # 2. Quartile Deviation:
 Measure # 3. Average Deviation (A.D.) or
Mean Deviation (M.D.):
 Measure # 4. Standard Deviation or S.D. and
Variance:

11.  The range is the simplest measure of spread
and is the difference between the highest and
lowest scores in a data set. In other words we
can say that range is the distance between
largest score and the smallest score in the
distribution.

12. The values that divide the given set of data into four
equal parts is called quartiles, and is denoted by Q1,
Q2, and Q3.

13. MAD= mean average deviation

14.  Standard deviation is the most commonly used and
the most important measure of variation. It
determines whether the scores are generally near or
far from the mean.

23.  It cannot be negative.
 It is only used to measure spread or
dispersion around the mean of a data set.
 For data with almost the same mean, the
greater the spread, the greater the
standard deviation.

24.  Variance describes how much a
random variable differs from its
expected value.

28. Mp = middle point

29.  One way of presenting out how data
are distributed is to plot them in a
graph.
 If the data is evenly distributed, our
graph will come across a curve.
 In statistics this curve is called a
normal curve.

31.  Skewness tells us about the amount and
direction of the variation of the data set.
 It is a measure of symmetry (evenness).
 A distribution or data set is symmetric if
it looks the same to the left and right of
the central point.

32.  Kurtosis is a parameter that describes the shape of
variation.
 It is a measurement that tells us how the graph of the
set of data is peaked and how high the graph is around
the mean. In other words we can say that kurtosis
measures the shape of the distribution.
 The concept of kurtosis is very useful in decision-
making.

33. Kurtosis has three types,
 mesokurtic, platykurtic, and leptokurtic.
 If the distribution has kurtosis of zero, then the graph
is nearly normal. This nearly normal distribution is
called mesokurtic.
 If the distribution has negative kurtosis, it is called
platykurtic.
 If the distribution has positive kurtosis, it is called
leptokurtic.

35.  The coefficient of variation is another useful
statistics for measuring dispersion of a data
set.