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)
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

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/( 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 Deviationμ = 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 statistical inference.

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. 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

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