Unit 2 Fundamentals of Statistics

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

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

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

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

Describing the Data Graphical Analytical

Frequency Distribution Ungrouped data Grouped data Tally sheet Histograms

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

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,

Tally Sheet Sample (Excel) 2.002 IIIII IIII 9 2.021 IIIII IIIII II 12 2.043 IIIII II 7 2.048 IIIII IIIII III 13 2.051 2.057 IIIII IIIII 10 2.064

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

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

Kurtosis

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

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

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

Computing Standard Deviation μ = σ =

Other Measures: Skewness

Other Measures Skewness

Other Measures: Kurtosis

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 statistical inference.

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

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

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

The Normal Curve Principle: The Standard Score 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

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

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