This presentation introduces probability, statistics, and their applications in engineering. It discusses key concepts such as random experiments, outcomes, and relative frequency in probability. In statistics, it explains how data is collected, organized, and analyzed to draw conclusions about populations. It then gives examples of how statistics is used in engineering to perform tests, collect data on product performance, and reveal information about quality. The presentation also outlines common statistical techniques like frequency distribution, cumulative frequency, variance, and normal distribution.

1. Welcome to ourWelcome to our
groupgroup
presentationpresentation
green university of Bangladeshgreen university of Bangladesh
presented Bypresented By
shufal Barmon-163010061shufal Barmon-163010061
mst. niva akter-163010134mst. niva akter-163010134
md. monoWar hasan-163010129md. monoWar hasan-163010129

2. proBaBilityproBaBility
andand
statistics instatistics in
engineeringengineering

3. Presentation LayoutPresentation Layout
► Basic idea of Probability
► Basic idea of Statics
► Statistics in Engineering
► Frequency Distribution
► Cumulative Frequency
► Variance
► Normal Distribution

4. Probability: Basic IdeasProbability: Basic Ideas
 Terminology:Terminology:

Trial:Trial: each time you repeat aneach time you repeat an
experimentexperiment

Outcome:Outcome: result of an experimentresult of an experiment

Random experiment:Random experiment: one with randomone with random
outcomes (cannot be predicted exactly)outcomes (cannot be predicted exactly)

Relative frequency:Relative frequency: how many times ahow many times a
specific outcome occurs within thespecific outcome occurs within the
entire experiment.entire experiment.

5. Statistics: Basic IdeasStatistics: Basic Ideas
 Statistics is the area of science that deals withStatistics is the area of science that deals with
collection, organization, analysis, andcollection, organization, analysis, and
interpretation of data.interpretation of data.
 It also deals with methods and techniques thatIt also deals with methods and techniques that
can be used to draw conclusions about thecan be used to draw conclusions about the
characteristics of a large number of data points--characteristics of a large number of data points--
commonly called acommonly called a populationpopulation----
 By using a smaller subset of the entire data.By using a smaller subset of the entire data.

6. For Example…For Example…
 You work in a cell phone factory and are askedYou work in a cell phone factory and are asked
to remove cell phones at random off of theto remove cell phones at random off of the
assembly line and turn it on and off.assembly line and turn it on and off.
 Each time you remove a cell phone and turn itEach time you remove a cell phone and turn it
on and off, you are conducting aon and off, you are conducting a randomrandom
experiment.experiment.
 Each time you pick up a phone is aEach time you pick up a phone is a trialtrial and theand the
result is called anresult is called an outcomeoutcome..
 If you check 200 phones, and you find 5 badIf you check 200 phones, and you find 5 bad
phones, thenphones, then
 relative frequencyrelative frequency of failure = 5/200 = 0.025of failure = 5/200 = 0.025

7. Statistics in EngineeringStatistics in Engineering
 Engineers apply physicalEngineers apply physical
and chemical laws andand chemical laws and
mathematics to design,mathematics to design,
develop, test, anddevelop, test, and
supervise varioussupervise various
products and services.products and services.
 Engineers perform testsEngineers perform tests
to learn how thingsto learn how things
behave under stress, andbehave under stress, and
at what point they mightat what point they might
fail.fail.

8. Statistics in EngineeringStatistics in Engineering
 As engineers perform experiments, theyAs engineers perform experiments, they
collect data that can be used to explaincollect data that can be used to explain
relationships better and to revealrelationships better and to reveal
information about the quality of productsinformation about the quality of products
and services they provide.and services they provide.

9. Cumulative FrequencyCumulative Frequency
 The data can be further organized by calculating theThe data can be further organized by calculating the
cumulative frequencycumulative frequency (CDF)(CDF)..
 The cumulative frequency shows the cumulative numberThe cumulative frequency shows the cumulative number
of students with scores up to and including those in theof students with scores up to and including those in the
given range. Usually we normalize the data - divide 26.given range. Usually we normalize the data - divide 26.

10. VarianceVariance
 Another way of measuring the data is byAnother way of measuring the data is by
calculating thecalculating the variancevariance..
 Instead of taking the absolute values ofInstead of taking the absolute values of
each deviation, you can just square theeach deviation, you can just square the
deviation and find the means.deviation and find the means.
 (n-1) makes estimate unbiased(n-1) makes estimate unbiased
v = i=1
n
∑ (xi −x)2
n −1

11.  Taking the square root of the varianceTaking the square root of the variance
which results in thewhich results in the standard deviation.standard deviation.
 The standard deviation can also provideThe standard deviation can also provide
information about the relative spread of ainformation about the relative spread of a
data set.data set.
s = i=1
n
∑ (xi −x)2
n −1

12.  The mean for a grouped distribution is calculatedThe mean for a grouped distribution is calculated
from:from:
 WhereWhere
xx = midpoints of a given range= midpoints of a given range
ff = frequency of occurrence of data in the range= frequency of occurrence of data in the range
nn == ∑∑ff = total number of data points= total number of data points
x =
(xf )∑
n

13. The standard deviation for a grouped distribution isThe standard deviation for a grouped distribution is
calculated from:calculated from:
s =
(x −x)2
f∑
n −1

14. Normal DistributionNormal Distribution
 We could use the probability distribution from the figuresWe could use the probability distribution from the figures
below to predict what might happen in the future. (i.e.below to predict what might happen in the future. (i.e.
next year’s students’ performance)next year’s students’ performance)

15. Normal DistributionNormal Distribution
 Any probability distribution with a bell-shapedAny probability distribution with a bell-shaped
curve is called acurve is called a normal distributionnormal distribution..
 The detailed shape of a normal distributionThe detailed shape of a normal distribution
curve is determined by its mean and standardcurve is determined by its mean and standard
deviation values.deviation values.