1 / 27

Fundamentals of Statistics: Collection and Analysis of Data

This unit explores the definitions and concepts of statistics, including the collection and analysis of quantitative data. Topics covered include variables and attributes, measurements and attributes in quality, frequency distribution, measures of central tendency and dispersion, and the normal curve.

lgunther
Download Presentation

Fundamentals of Statistics: Collection and Analysis of Data

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Unit 2 Fundamentals of Statistics

  2. Definitions of Statistics • A collection of quantitative data.... • Science of systematic gathering and analysis... of data.....

  3. Collection of Data • Variables (measurable quality characteristics): • Lengths • Voltage • Resistance • Attributes (conforming or nonconforming quality characteristics): • go/no go gage • Visual inspection of painted products

  4. Some Measurements in quality Dimensional Volume Ages Temperatures Sound Rate Voltage Numbers Angles Resistance Brightness Time Hardness Roundness Distance Speed Roughness Humidity Weight Thickness Height

  5. Some Attributes in quality • Finish • Smoothness • Go/No-Go Inspection • Yes-No Inspection

  6. Describing the Data • Graphical • Analytical

  7. Frequency Distribution • Ungrouped data • Grouped data • Tally sheet • Histograms

  8. Sale Of Shoes Of Various Sizes At A Shop (Ungrouped Data) • 7  8  5  4  9  8  5  7  6  8  9  6  7  9 • 8  7  9  9  6  5  8  9  4  5  5  8  9  6

  9. Marks Obtained By 40 Students In An Examination (Grouped Data) • 3, 3, 5, 8, 9, 10, 11, 12, 13, 15, 17, 17, 17, 19, 19, 19, 20, 21, 21, 23, 23, 25, 25, 28, 28, 32, 32, 32, 33, 34, 34, 36, 37, 39, 39, 41, 45, 46, 48, 48,

  10. Tally Sheet Sample (Excel)

  11. Steps In Preparing And Presenting Grouped Data Collect data and prepare a tally sheet Data sheet Tally sheet Determine the range R = Xh – Xl (R = range; Xh = Highest number; Xl = Lowest number) Determine the cell interval i = R/(1 + 3.322 log n) Determine the cell mid point MPl = Xl + i/2 Determine the cell boundaries Post the cell frequency

  12. Characteristics of Frequency Distribution Graphs • Population frequency distribution • Sample frequency distribution • Analysis of histograms • Symmetry • Modal characteristics • Leptokurtic • Platycurtic

  13. Kurtosis

  14. Measures of Central Tendency • Average: 1, 3, 3, 5, 5, 5, 6, 7, 7, 8, 11 • Median: 1, 3, 3, 5, 5, 5, 6, 7, 7, 8, 11 • Mode: 1, 3, 3, 5, 5, 5, 6, 7, 7, 8, 11

  15. Relationship Among the Measures of Central Tendency • All are identical when there is symmetrical distribution • Average is the most commonly used measure of central tendency • Median is effective when distribution is skewed • Mode is use to determine the most likely value of a distribution

  16. Relationship Among the Measures of Dispersion • The range is very simple to calculate, and ideal when the amount of data is too small or too scattered • The accuracy of the range decreases as the number of observations increases • The standard deviation is ideal for more precise measure of variation • As the standard deviation gets smaller, the quality gets better

  17. Computing Standard Deviation μ = σ =

  18. Other Measures: Skewness

  19. Other Measures • Skewness

  20. Other Measures: Kurtosis

  21. Concept of a Population and a Sample Sampling is that part of statistical practice concerned with the selection of a subset of individual observations within a population of individuals intended to yield some knowledge about the population of concern, especially for the purposes of making predictions based on statisticalinference.

  22. Concept of a Population and a Sample • The selected members are called the Sample • The group from which the sample was selected is called the Population

  23. Concept of a Population and a Sample • Sample is represented by a histogram • Population is represented by a normal curve • The Normal Curve (or Bell Curve) results from this distribution

  24. The Normal Curve (or Bell Curve) Principle • Is a graph representing the density function of the normal probability distribution • Also referred to as the Normal Curve or Bell Curve • To draw a normal curve, one needs to specify the mean and the standard deviation • The curve is made up of 6 standard deviations • A Normal distribution with a mean of zero and a standard deviation of 1 is known as the Standard Normal Distribution

  25. Often raw scores are converted to standard scores Standard scores are represented by the letter “Z” 6 standard deviations are equal to 99.6% of the area within the normal curve The Normal Curve Principle: The Standard Score

  26. Standardized normal value “z” or Standard Score The standard score is where: x is a raw score to be standardized; μ is the mean of the population; σ is the standard deviation of the population

  27. Applications of the Normal curve Principles • In quality control • In statistics • In business management • In every discipline known to man

More Related