Lecture 1
Stage: Second
Subject: Engineering Statistics
Statistics: Introduction
Definitions
Statistics
Collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions.
Variable
Characteristic or attribute that can assume different values
Random Variable
A variable whose values are determined by chance.
Population
All subjects possessing a common characteristic that is being studied.
Sample
A subgroup or subset of the population.
Parameter
Characteristic or measure obtained from a population.
Statistic (not to be confused with Statistics)
Characteristic or measure obtained from a sample.
Descriptive Statistics
Collection, organization, summarization, and presentation of data.
Inferential Statistics
Generalizing from samples to populations using probabilities. Performing hypothesis testing, determining relationships between variables, and making predictions.
Qualitative Variables
Variables which assume non-numerical values.
Quantitative Variables
Variables which assume numerical values.
Discrete Variables
Variables which assume a finite or countable number of possible values. Usually obtained by counting.
Continuous Variables
Variables which assume an infinite number of possible values. Usually obtained by measurement.
Nominal Level
Level of measurement which classifies data into mutually exclusive, all inclusive categories in which no order or ranking can be imposed on the data.
Ordinal Level
Level of measurement which classifies data into categories that can be ranked. Differences between the ranks do not exist.
Interval Level
Level of measurement which classifies data that can be ranked and differences are meaningful. However, there is no meaningful zero, so ratios are meaningless.
Ratio Level
Level of measurement which classifies data that can be ranked, differences are meaningful, and there is a true zero. True ratios exist between the different units of measure.
Random Sampling
Sampling in which the data is collected using chance methods or random numbers.
Systematic Sampling
Sampling in which data is obtained by selecting every k the object.
Convenience Sampling
Sampling in which data is which is readily available is used.
Stratified Sampling
Sampling in which the population is divided into groups (called strata) according to some characteristic. Each of these strata is then sampled using one of the other sampling techniques.
Cluster Sampling
Sampling in which the population is divided into groups (usually geographically). Some of these groups are randomly selected, and then all of the elements in those groups are selected.
Levels of Measurement
There are four levels of measurement: Nominal, Ordinal, Interval, and Ratio. These go from lowest level to highest level. Data is classified according to the highest level which it fits. Each additional level adds something the previous level didn t have.
• Nominal is the lowest level. Only names are meaningful here.
• Ordinal adds an order to the names.
• Interval adds meaningful differences
• Ratio adds a zero so that ratios are meaningful.
You can generate random numbers on the TI-82 calculator using the following sequence. N is the number of different values which could be and S is the minimum number.
INT (N*rand+S)
INT is found under the MATH menu (math num 4). RAND is also found under the MATH menu (math prb 1).
Simulate the rolling of a die (1-6): int (6*rand+1)
Simulate the flipping of a coin (0-1): INT (2*rand)
This works because the rand function returns a random number between 0 and 1 (including 0 but not including 1). When it is multiplied by N, it becomes between 0 and N, and then S is added, so it becomes between S and S+N.
If you have two values (A and B) that you need random numbers between, then you can generate them using the following formulas.
N=B-A+1
INT (N*rand+A)
Notice it is B-A+1 not B-A. Everyone agrees there are 10 numbers between 1 and 10 (inclusive). But, if you take 10-1, you get 9, not 10. Also, in the formula above, replace the N by the actual number of different values.
Since the calculator remembers the last formula put in, and evaluates it when you hit enter, to generate more random numbers, just hit enter again. Each time you hit enter, you will get another random number.
The purpose of this laboratory exercise is to familiarize yourself with the different sampling techniques.
You need one page from a movie listing (like contained in TV-Guide). Note, if you actually use TV Guide®, then you need to use two facing pages. Pick a page with little extraneous material, other than the listings, on it.
For the purposes of this sampling project, a movie is included on the page or in a cluster if the running time for the movie falls on the page.
Random Sampling
Number each movie on the page. If there are a lot of movies, you may wish to number every other or every third movie.
Generate a random sample on 8 numbers between 1 and the number of movies on the page. Write down the # generated and the running time for the movie corresponding to that number.
Systematic Sampling
Generate a random number between 1 and 6. Beginning with the movie corresponding to that number, and then taking every 6th movie thereafter, write the # of the movie and the running length of the movie.
Convenience Sampling
White down the running time of the first eight movies.
Stratified Sampling
On a separate piece of paper, write down the running times of all PG/PG13, R, and not-rated (either NR or no rating given) movies in three columns -- ignore all other types (NC17, G, etc). Split a sample of 8 proportionally to each type of movie (if R is 40%, then sample 40% of 8 = 3.2 -> 3 R movies). Use random sampling within each movie type. Record the running lengths of the movies selected.
Cluster Sampling
Divide the page into equal regions so that each region has roughly 3-4 movies in each cluster. Randomly select 3 clusters, and record the running length of all movies in those clusters.
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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