Ch1 The Nature of Statistics

STATISTICS FOR ENGINEERS AND SCIENTISTS

1. STATISTICS FOR ENGINEERS
AND SCIENTISTS
Farhan Alfin
Chapter 1:
The Nature of Statistics

2. Objectives
Introduction of some basic
statistical terms.
Introduction of some graphical
displays.

3. Introduction
What is statistics?Statisticsis the
science of conducting studies to
collect, organize, summarize,
analyze, and draw conclusions
The subject of statistics is divided
into two broad areas—descriptive
statistics ءاصحايفصو and inferential
statistics ءاصحايئارقتسا .

4. Descriptive & Inferential
Statistics
Descriptive Statisticsconsists of the
collection, organization, summarization,
and presentation of data
Inferential Statisticsconsists of general-
izing from samples to populations, per-
forming hypothesis testing, determining
relationships among variables, and
making predictions

5. Statistics
Descriptive
Statistics
Inferential
Statistics
Includes
Collecting
Organizing
Summarizing
Presenting data
Includes
Making inferences
Hypothesis testing
Determining
relationships
Making predictions
Breakdown of the subject of statistics

6. Population and Sample
•In order for statisticians to do any
analysis, data must be collected or
sampled.
•We can sample the entire population or
just a portion of the population.
•What is a population?A population
consists of all elements that are being
studied.
•What is a sample?: A sample is a subset
of the population.

7. Population and Sample

8. Variables and Data
A variableis a characteristic or attribute that
can assume different values
Data are the values that variables can
assume
A data setis a collection of data values.
Each value in the data set is called a data
valueor a datum
Random variables ةيئاوشع تاريغتمhave values
that are determined by chance

9. Variables & Types of Data
Qualitative Variablescan be placed into
distinct categories according to some
characteristic or attribute. For example,
gender (male or female). Type of
organism or type of wheat .
These are variables that are
nonnumeric in nature.

10. Variables & Types of Data
Quantitative Variables ةيمك تاريغتمare
numerical in nature and can be ordered or
ranked. Example:age (1000 kernel weight
or pH values)is numerical and the values
can be ranked,the heights of female
basketball players.
These are variables that can assume
numeric values.
Quantitativevariables can be classified
into two groups –discrete ةعطقتم
variables and continuous ةرمتسم
variables.

11. Variables & Types of Data
Discrete Variablesassume values that
can be counted.
•Example:the number of broken
kernel in wheat sample.
Continuous Variablescan assume all
values between any two specific values.
They are obtained by measuring.
•Example:the time it takes to
complete a reaction (or, test weight
of Cereal).

12. Variables
Quantitative Qualitative
Includes
Discrete
Continuous variables
Breakdown of the types of variables

13. Organizing Data
When data are collected in original
form, they are calledraw data.
When the raw data is organized into a
frequency distribution, the frequencywill
be the number of values in a specific
class of the distribution.

14. Organizing Data
Afrequency distributionis the
organizing of raw data in table form,
using classes and frequencies.
What is a frequency count?The
frequency or the frequency count for
a data value is the number of times
the value occurs in the data set.

15. Categorical or Qualitative
Frequency Distributions
•NOTE:We will consider categorical,
ungrouped, and grouped frequency
distributions.
What is a categorical frequency
distribution?A categorical frequency
distribution represents data that can be
placed in specific categories, such as
gender, hair color, political affiliation etc.

16. Categorical or Qualitative
Frequency Distributions --Example
•Example:The blood types of 25 blood donors
are given below. Summarize the data using a
frequency distribution.
AB B A O B
O B O A O
B O B BB
A O AB ABO
A B AB O A

17. Categorical Frequency Distribution
for the Blood Types-Example
Continued
Note:The classes for the distribution
are the blood types.

18. Quantitative Frequency
Distributions --Ungrouped
•What is an ungrouped frequency
distribution?An ungrouped frequency
distribution simply lists the data values
with the corresponding frequency counts
with which each value occurs.

19. Quantitative Frequency Distributions
–Ungrouped --Example
•Example:The at-rest pulse rate for 16
athletes at a meet were 57, 57, 56, 57,
58, 56, 54, 64, 53, 54, 54, 55, 57, 55, 60,
and 58. Summarize the information with
an ungrouped frequency distribution.

20. Quantitative Frequency
Distributions –Ungrouped --
Example Continued
Note:The
(ungrouped)
classes are
the observed
values
themselves.

21. Relative Frequency
•NOTE:Sometimes frequency
distributions are displayed with relative
frequencies as well.
•What is a relative frequency for a class?
The relative frequency of any class is
obtained dividing the frequency (f)for
the class by the total number of
observations (n).

22. Relative Frequency
Example:The relative frequencyfor the ungrouped
class of 57will be 4/16 = 0.25.ondistributi the in nsobservatio of number total
class the for frequency
class a for Frequency Relative 

23. Relative Frequency
Distribution
Note:The relative
frequency for a
class is obtained
by computing f/n.

24. Cumulative Frequency and
Cumulative Relative Frequency
•NOTE:Sometimes frequency
distributions are displayed with
cumulative frequencies and
cumulative relative frequencies as
well.

25. Cumulative Frequency and
Cumulative Relative Frequency
•What is a cumulative frequency for
a class?The cumulative frequency
for a specific class in a frequency
table is the sum of the frequencies
for all values at or below the given
class.

26. Cumulative Frequency and
Cumulative Relative Frequency
What is a cumulative relative
frequency for a class?The
cumulative relative frequency for a
specific class in a frequency table
is the sum of the relative
frequencies for all values at or
below the given class.

27. Cumulative Frequency and
Cumulative Relative Frequency
Note:Table
with
relative and
cumulative
relative
frequencies.

28. Quantitative Frequency
Distributions --Grouped
What is a grouped frequency
distribution?A grouped frequency
distribution is obtained by
constructing classes (or intervals)
for the data, and then listing the
corresponding number of values
(frequency counts) in each interval.

29. Quantitative Frequency
Distributions --Grouped
•There are several procedures that
one can use to construct a grouped
frequency distribution.
•However, because of the many
statistical software packages
(MINITAB, SPSS etc.) and
graphing calculators (TI-83 etc.)
available today, it is not necessary
to try to construct such
distributions using pencil and paper.

30. Histograms, Frequency
Polygons, and Ogives
The three most commonly used
graphs in research are:
The histogram.
The frequency polygon.
The cumulative frequency graph, or
ogive (pronounced o-jive).

31. Histogram
The histogramis a graph that
displays the data by using vertical
bars of various heights to represent
the frequencies.

32. Example of a Histogram80797877767574737271
10
5
0
Wheat Test weight (Kg/HL)
Frequency

33. Frequency polygon
A frequency polygonis a graph that
displays the data by using lines that
connect points plotted for frequencies
at the midpoint of classes. The
frequencies represent the heights of
the midpoints.

34. Example of a Frequency Polygon80797877767574737271
10
5
0
Wheat Test weight (Kg/HL)
Frequency

35. Ogive
A cumulative frequency graphor
ogiveis a graph that represents the
cumulative frequencies for the
classes in a frequency distribution.

36. Example of an Ogive80797877767574737271
50
40
30
20
10
0
Wheat Tsst Weight (Kg/HL)
Cumulative Frequency

37. Time series graph
Time series graph -A time series
graph represents data that occur over
a specific period of time.

38. Time Series Graph2003200119991997199519931991
5000
4000
3000
2000
(1000xton)Syria wheat production

39. Pie graph
Pie graph -A pie graph is a circle that
is divided into sections or wedges
according to the percentage of
frequencies in each category of the
distribution.

40. Pie graphEmbryo ( 1.0%)
Aleron ( 7.0%)
scutellum ( 1.5%)
Pericarp ( 8.0%)
Out Endosper (12.5%)
Mid Endosper (12.5%)
In Endosperm (57.5%)
Percentage of Wheat Kernel parts