# Introduction to Statistics Descriptive Statistics by q8a1ML

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```									  Introduction to Statistics
Descriptive Statistics

Statistics Terminology
Scales of Measurements
Measures of Central
Tendencies
Skewness
Measures of Variability
Statistics: The Course
 Descriptive       Inferential
Statistics         Statistics
Deals with         Deals with data
describing data    collected from
that has been      samples so one
collected.         can generalize
to populations.
Populations vs Samples
 Population        Sample
A population       A sample is a
consists of all    subset of a
members of         population. It
some specified     has the same
group.             characteristics
as the
population.
Parameters vs Statistics
 Parameters          Statistic
A measure of a       A measure of a
characteristic of    characteristic
an entire            of a sample.
population.
Parameters vs Statistics
In research, we obtain information about
population parameters by using
information from samples that represent
the population.
We apply the laws of probability to the
data collected from the samples to
generalize to the population..
Populations versus Samples
 Population – all the people or things
involved in a particular study
 Sample – a subset of a population
 Samples are used to estimate the population
value of some parameter.
 A population characteristic under study is a
population parameter. It is estimated
using a sample statistic.
Measures of Central
Tendencies
What is happening around the center of the
data?
Mean: the arithmetic average
Median: the point where 50% of the
data is above and 50% is below
Mode: occurs most frequently
The Mode

 The value that occurs most frequently
 Is the simplest of the central tendencies.
 No computation is required.
 Very unstable information about the data
 Only average that can be used with
nominal data.
The Median

 The point at which 50% of the data is
above and 50% is below
 Data is sorted and middle point is found.
 Is not sensitive to extreme scores.
 It is not appropriate to average median
scores.
The Mean

   The arithmetic average
   Add the values (data) and divide by the
number of values
   Takes into account the value of every data
point.
   Is considered the most stable central tendency.
Measures of Variability

 Variabilitymeasures describe the
distribution of the data.
 Examples:
Range
Standard Deviation
The Range

 Simplest measure of variability
 (Highest value minus the lowest value)
plus 1
 Unreliable because it is based on only two
values
The Standard Deviation

 Very useful measure of variability
 Shows the difference between a raw score
and the mean of a set of data.
 All the data is included in its
computation.
Skewness
Describes visually the distribution of
the data.
Examples:
Symmetrical distribution: two halves
of data are mirror images.
Skewed distribution: Data is pulled
by extreme scores to the left or right.
Symmetrical Distribution
6
5
4
3
2
1
0
1   2   3   4   5   6   7
Skewed Distributions
Hint: The tail points to the skew.

Negatively Skewed           6
5
4

Median right of mean        3
2
1
0
More high scores                1   2   3       4       5       6       7

6
5

Positively Skewed           4
3
2

Median left of mean         1
0
1   2   3   4       5       6       7

More low scores
The End

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