Engineering Data Analysis

ENGINEERING DATA ANALYSIS statistical population to estimate characteristics
of the whole population.
Lesson 1: Data Collection

EXPERIMENTATION
Data Collection – is a systematic way of gathering On the other hand, experimentation is the
and measuring information on different groups collection of data in a more controlled
of people. The data collected can be used on manner. One example is the data you collected as
research, testing hypothesis, and other intended a result of your laboratory experiments. Kindly
purposes. note that the experimentation process is not
Regression analysis is a widely used limited inside a laboratory. Most of the
technique of statistical inference used to companies use experimentation in order to test
determine the strength and nature of the their hypothesis. For example, a company can
relationship (the correlation) between a launch a sales competition to test how
dependent variable and one or more salespeople react to different levels of
explanatory (independent) variables. The performance incentives.
output of a regression model is often
analyzed for statistical significance, which
refers to the claim that a result from findings
generated by testing or experimentation is Lesson 2: Introduction to Probability
not likely to have occurred randomly or by
chance. It's likely to be attributable to a Probability - is a measure of the likelihood
specific cause elucidated by the data. that a particular event will occur. To compute the
probability of a particular event to happen:
TYPES OF DATA Probability of an event = (number of ways it

can happen) / (total number of outcomes)
1. Quantitative - sets of data in numerical form,
can be either counted or measured. If an event is certain to happen, Probability = 1. If
• Discrete Data - data that can be an event is impossible to happen, the Probability
"counted" (e.g., No. of Pencils, No. of of that event = 0. Therefore, the Probability value
People) is ranging from 0 to 1.
• Continuous Data - data can be Probability can be expressed into a decimal,
"measured" (e.g. Height, Weight, and fraction, or percentage. Let's take a look at these
Temperature) examples:
2. Qualitative - sets of data that is more on
characteristics and classification
Lesson 2.1: Basic Rules of Combining
• Binary Data - falls under two Probabilities
mutually exclusive categories (e.g.
right/wrong, true/false) There are basic rules to follow on combining
• Nominal Data -named categories probabilities:
with no specific rank or order (e.g.
blue/red/green) 1. ADDITION RULE
• Ordinal Data - categories with specific
rank or natural order (e.g. short, medium, (a) If the events are mutually exclusive, there is no
tall) overlap: if one event occurs, other events cannot
Note: Data collection involves either occur. In that case, the probability of occurrence
sampling or experimentation. of one or another of more than one event is
the sum of the probabilities of the separate
SAMPLING events. Mutually exclusive events mean two or
If you are collecting data about a group of more events cannot happen at the same time.
people, say, about 10 students. It is easy to tally
and record them accordingly. But if the statistical (b) If the events are not mutually exclusive, there
population is too large to survey, it is better to can be overlap between them. This can be
use gather data within a sample size only. This visualized using a Venn diagram. The probability
process is called sampling. Sampling is the
selection of a subset of individuals from within a
of overlap must be subtracted from the sum be used. The conditional probability of B given
of probabilities of the separate events that A occurs, or on condition that A occurs, is
written P [B | A].This is read as the probability
Set Relations on Venn Diagram of B given A, or the probability of B on
Let's look at the Venn diagram (b) and (c) condition that A occurs.
• P [A ∩ B) = P [occurrence of both A and B], Note: The multiplication rule for the occurrence
the intersection of events A and B. of both A and B together when they are not
independent is the product of the probability of
• P [A ∪ B) = P [occurrence of A or B or both], the one event and the conditional probability of the
union of the two events A and B. other:
P [A ∩ B] = P [A] × P [B | A] = P [B] × P [A | B]
•If two events being considered, A and B, are
not mutually exclusive, and so there may be the Lesson 3: Permutation and Combination
overlap between them, the Addition Rule
becomes P (A ∪ B) = P (A) + P (B) – P (A ∩ B) Permutation - is an arrangement of all or part
of a set of objects. The number of
If three events A, B, and C are not mutually permutations is the number of different
exclusive: arrangements in which items can be placed.
P (A ∪ B ∪ C) = P (A) + P (B) + P (C) – P (A ∩ B) – P Notice that if the order of the items is
(A ∩ C) – P (B ∩ C) + P (A ∩ B ∩ C) changed, the arrangement is different, so we have
a different permutation. In permutations, the
2. MULTIPLICATION RULE order is important!
(a) The basic idea for calculating the number • Rule1. The number of permutations of n
of ways can be described as follows: If an objects is n!
operation can be performed in n1 ways and if
for each of these ways a second operation can • Rule2. The number of permutations of n distinct
be performed in n₂ ways, then the two objects taken r at a time is nPr = n! / (n − r)!
operations can be performed together in n₁n₂
ways. • Rule3. If n items are arranged in a circle,
the arrangement doesn’t change if every item
Note: For more than two operations: If an is moved by one place to the left or the right.
operation can be performed in n₁ ways, and if Therefore in this situation, one item can be placed
for each of these a second operation can be at random, and all the other items are placed
performed in n₂ ways, and for each of the first concerning the first item. The number of
two a third operation can be performed in n₃ permutations of n objects arranged in a circle is (n
ways, and so forth, then the sequence of k − 1)!
operations can be performed in n₁n₂ ··· nk ways.
• Rule4. The number of distinct permutations of
(b) The simplest form of the Multiplication Rule n things of which n1 are of one kind, n2of a
for probabilities is as follows: If the events are second kind, ... , nk of a kth kind is
independent, then the occurrence of one
event does not affect the probability of
occurrence of another event. In that case, the
probability of occurrence of more than one event
together is the product of the probabilities of the
separate events. (This is consistent with the basic
idea of counting stated above.) If A and B are two
separate events that are independent of one Combinations - are similar to permutations, but
another, the probability of occurrence of both A with the important difference that
and B together is given by P [A ∩ B] = P [A] × P [B] combinations take no account of order. Thus,
AB and BA are different permutations but the
(c) If the events are not independent, one same combination of letters. Then the number
event affects the probability of the other of permutations must be larger than the
event. In this case, conditional probability must number of combinations, and the ratio
between them must be the number of ways
the chosen items can be arranged.
In general, the number of combinations of n
items taken r at a time is
Lesson 3.1: SAMPLING DISTRIBUTION
Population and Sample

Often in practice, we are interested in drawing
valid conclusions about a large group of
individuals or objects. Instead of examining
the entire group, called the population, which
may be difficult or impossible to do, we may
examine only a small part of this population,
which is called a sample. We do this with the
aim of inferring certain facts about the
population from results found in the sample, a
process known as statistical inference. The
process of obtaining samples is called
sampling. Let's take a look at these examples
below.
a. We may wish to draw conclusions about

the weights of 12,000 adult students (the
population) by examining only 100 students (a
sample) selected from this population.
b. We may wish to draw conclusions about

the percentage of defective bolts produced in
a factory during a given 6-day week by
examining 20 bolts each day produced at
various times during the day. In this case, all
bolts produced during the week comprise the
population, while the 120 selected bolts
constitute a sample.
c. We may wish to draw conclusions about

the fairness of a particular coin by tossing it
repeatedly. The population consists of all possible
tosses of the coin. A sample could be obtained by
examining, say, the first 60 tosses of the coin and
noting the percentages of heads and tails.
d. We may wish to draw conclusions about

the colors of 200 marbles (the population) in an
urn by selecting a sample of 20 marbles from
the urn, where each marble selected is
returned after its color is observed.

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ENGINEERING DATA ANALYSIS statistical population to estimate characteristics

of the whole population.

Lesson 1: Data Collection

TYPES OF DATA Probability of an event = (number of ways it

Lesson 3.1: SAMPLING DISTRIBUTION

Population and Sample

a. We may wish to draw conclusions about

b. We may wish to draw conclusions about

c. We may wish to draw conclusions about

d. We may wish to draw conclusions about

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