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## Quality Control

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**Quality Control**Chapter 4- Fundamentals of Statistics PowerPoint presentation to accompany Besterfield Quality Control, 8e PowerPoints created by Rosida Coowar**Outline**Introduction Frequency Distribution Measures of Central Tendency Measures of Dispersion**Outline-Continued**Other Measures Concept of a Population and Sample The Normal Curve Tests for Normality**Introduction**Definition of Statistics: • A collection of quantitative data pertaining to a subject or group. Examples are blood pressure statistics etc. • The science that deals with the collection, tabulation, analysis, interpretation, and presentation of quantitative data**Introduction**Two phases of statistics: • Descriptive Statistics: • Describes the characteristics of a product or process using information collected on it. • Inferential Statistics (Inductive): • Draws conclusions on unknown process parameters based on information contained in a sample. • Uses probability**Collection of Data**Types of Data: Attribute: Discrete data. Data values can only be integers. Counted data or attribute data. Examples include: • How many of the products are defective? • How often are the machines repaired? • How many people are absent each day?**Collection of Data – Cont’d.**Types of Data: Attribute: Discrete data. Data values can only be integers. Counted data or attribute data. Examples include: • How many days did it rain last month? • What kind of performance was achieved? • Number of defects, defectives**Collection of Data**Types of Data: Variable: Continuous data. Data values can be any real number. Measured data. Examples include: • How long is each item? • How long did it take to complete the task? • What is the weight of the product? • Length, volume, time**Precision and Accuracy**Precision The precision of a measurement is determined by how reproducible that measurement value is. For example if a sample is weighed by a student to be 42.58 g, and then measured by another student five different times with the resulting data: 42.09 g, 42.15 g, 42.1 g, 42.16 g, 42.12 g Then the original measurement is not very precise since it cannot be reproduced.**Precision and Accuracy**Accuracy • The accuracy of a measurement is determined by how close a measured value is to its “true” value. • For example, if a sample is known to weigh 3.182 g, then weighed five different times by a student with the resulting data: 3.200 g, 3.180 g, 3.152 g, 3.168 g, 3.189 g • The most accurate measurement would be 3.180 g, because it is closest to the true “weight” of the sample.**Precision and Accuracy**Figure 4-1 Difference between accuracy and precision**DescribingData**• Frequency Distribution • Measures of Central Tendency • Measures of Dispersion**Frequency Distribution**• Ungrouped Data • Grouped Data**Frequency Distribution**2-7 There are three types of frequency distributions • Categorical frequency distributions • Ungrouped frequency distributions • Grouped frequency distributions**Categorical**2-7 Categorical frequency distributions • Can be used for data that can be placed in specific categories, such as nominal- or ordinal-level data. • Examples - political affiliation, religious affiliation, blood type etc.**Categorical**Example :Blood Type Frequency Distribution 2-8**Ungrouped**2-9 Ungrouped frequency distributions • Ungrouped frequency distributions - can be used for data that can be enumerated and when the range of values in the data set is not large. • Examples - number of miles your instructors have to travel from home to campus, number of girls in a 4-child family etc.**Ungrouped**Example :Number of Miles Traveled 2-10**Grouped**2-11 • Grouped frequency distributions • Can be used when the range of values in the data set is very large. The data must be grouped into classes that are more than one unit in width. • Examples - the life of boat batteries in hours.**Grouped**Example: Lifetimes of Boat Batteries 2-12 Class Class Frequency Cumulative limits Boundaries frequency 24 - 37 23.5 - 37.5 4 4 38 - 51 37.5 - 51.5 14 18 52 - 65 51.5 - 65.5 7 25**Frequency Distributions**Table 4-3 Different Frequency Distributions of Data Given in Table 4-1**The Histogram**The histogram is the most important graphical tool for exploring the shape of data distributions. Check: http://quarknet.fnal.gov/toolkits/ati/histograms.html for the construction ,analysis and understanding of histograms**Constructing a Histogram**The Fast Way Step 1: Find range of distribution, largest - smallest values Step 2: Choose number of classes, 5 to 20 Step 3: Determine width of classes, one decimal place more than the data, class width = range/number of classes Step 4: Determine class boundaries Step 5: Draw frequency histogram**Constructing a Histogram**Number of groups or cells • If no. of observations < 100 – 5 to 9 cells • Between 100-500 – 8 to 17 cells • Greater than 500 – 15 to 20 cells**Constructing a Histogram**For a more accurate way of drawing a histogram see the section on grouped data in your textbook**Other Types of Frequency Distribution Graphs**• Bar Graph • Polygon of Data • Cumulative Frequency Distribution or Ogive**Characteristics of FrequencyDistribution Graphs**Figure 4-6 Characteristics of frequency distributions**Analysis of Histograms**Figure 4-7 Differences due to location, spread, and shape**Analysis of Histograms**Figure 4-8 Histogram of Wash Concentration**Measures of Central Tendency**The three measures in common use are the: • Average • Median • Mode**Average**There are three different techniques available for calculating the average three measures in common use are the: • Ungrouped data • Grouped data • Weighted average**Average-Grouped Data**h = number of cells fi=frequency Xi=midpoint**Average-Weighted Average**Used when a number of averages are combined with different frequencies**Median-Grouped Data**Lm=lower boundary of the cell with the median N=total number of observations Cfm=cumulative frequency of all cells below m Fm=frequency of median cell i=cell interval**Example Problem**Table 4-7 Frequency Distribution of the Life of 320 tires in 1000 km**Median-Grouped Data**Using data from Table 4-7**Mode**The Mode is the value that occurs with the greatest frequency. It is possible to have no modes in a series or numbers or to have more than one mode.**Relationship Among theMeasures of Central Tendency**Figure 4-9 Relationship among average, median and mode**Measures of Dispersion**• Range • Standard Deviation • Variance**Measures of Dispersion-Range**The range is the simplest and easiest to calculate of the measures of dispersion. Range = R = Xh - Xl • Largest value - Smallest value in data set**Measures of Dispersion-Standard Deviation**Sample Standard Deviation:**Standard Deviation**Ungrouped Technique**Standard Deviation**Grouped Technique**Relationship Between the Measures of Dispersion**• As n increases, accuracy of R decreases • Use R when there is small amount of data or data is too scattered • If n> 10 use standard deviation • A smaller standard deviation means better quality