Data Representation: Stem-and-Leaf Plots and Frequency Distribution, Lecture notes of Data Analysis & Statistical Methods

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Lecture 1

Introduction to Statistics

and Data Analysis

(Obtaining Data)

MathEng3-M (Engineering Data Analysis)

Outline of Discussion (Lecture1)

➢ Introduction to Statistics and Data Analysis

➢ Summary Statistics

➢ Graphical Summaries

The Challenge ❑ With the advancement in sciences and engineering occurring in large part through the collection and analysis of data, proper analysis of data can be challenging, because scientific data are subject to random variation. ❑ How can one draw conclusions from the results of an experiment when those results could have come out differently? ❑ The method of statistics allow scientists and engineers to design valid experiments and to draw reliable conclusions from the data they produce.

THE ENGINEERING METHOD AND STATISTICAL THINKING

The Basic Idea The basic idea behind all statistical methods

of data analysis is to make inferences about a

population by studying a relatively small

sample from it.

The Basic Idea For example, consider a machine that makes steel balls for ball bearings used in clutch systems. The specification for the diameter of the balls is 0. 65 ± 0. 03 cm. During the last hour, the machine has made 2000 balls. The QE wants to know how many of these balls meet the specifications. He does not have the time to measure all 2000 balls, so he draws a random sample of 80 balls, 72 of which ( 90 %) meet the specifications. (How can he be sure that 90 % of the whole population meet the specifications)?

➢ INFERENTIAL STATISTICS is the process of using data analysis to make predictions (“inference”) from that data. ➢ DESCRIPTIVE STATISTICS are used to describe the basic features in the study, in the form of charts, graphs, plots, etc. TWO FIELDS OF STATISTICS

COLLECTING ENGINEERING DATA

Sampling

A simple random sample of size n is a sample chosen by a

method in which each collection of n population items is

equally likely to comprise the sample, just as in a lottery. Think of a lottery consisting of 10 , 000 tickets and 5 winners will be chosen. What is the fairest way to choose the winners?

Sampling Example: A utility company wants to conduct a survey to measure the satisfaction level of its customers in a certain town. There are 10,000 customers in the town, and utility employees want to draw a sample of size 200 to interview personally. They obtain a list of all 10,000 customers, and number them from 1 to 10,000. They use a computer random number generator to generate 200 random integers between 1 and 10,000 and then contact the customers who correspond to those numbers. Is this a simple random sample?

Example: A construction engineer has just received a shipment of 1000 concrete blocks, each weighing approximately 25 kilograms. The blocks have been delivered in a large pile. The engineer wishes to investigate the compressive strength of the blocks by measuring the strengths in a sample of blocks. What is the more appropriate method of selecting random samples?

A sample of convenience is a sample that is not drawn by a well-defined random method. SAMPLE OF CONVENIENCE

A sampling variation happens when two or more different samples from the same population will differ from each other as well. SAMPLING OF VARIATION

➢ With sampling with replacement, what one gets in one sample does not affect what one gets in a different sample. In this case, we say that the samples are independent. ➢ With sampling without replacement, what one gets in one sample does affect what one gets in a different sample. In this case, we say that the samples are dependent. SAMPLING