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Session IV
“Fundamentals of Statistics”
Fundamentals of Statistics
Definitions
Frequency Distribution
Measures of Central Tendency
Measures of Dispersion
Other Measures
Concept of a Population and Sample
The Normal Curve
Tests for Normality
Scatter Diagram
Computer Applications• EXCEL will solve for average, median, range, standard
deviation, frequency, kurtosis, skewness, normal distribution, Z test, weibull distribution, and correlation. Histogram with descriptive statistics is an add-in under Tools/Data Analysis.
• EXCEL program files on the website will solve for chi-squared, and scatter diagram.
Definition of Statistics
A collection of quantitative data pertaining to a
subject or group.
The science that deals with the collection, tabulation,
analysis, interpretation, and presentation of
quantitative data
Definition of Statistics
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.
Probability
Types of DataAttribute
• Discrete data
• Data values can only be integers
• Counted data or attribute data
Examples include:
Number of defected products
Number of repaired machines
Number of absent students
Number of raining days last month
Types of Data
Variables
• Continuous data
• Data values can be any real number
• Measured data
Examples include: Lengths of items
Time needed to complete a task
Weight of a product
Length, volume, time.
Significant Figures
Significant Figures = Measured numbers
When you measure something there is always room for a little
bit of error
5 ft. 9 inches may be 5 ft. 9.01 inches?
Counted numbers and defined numbers ( 12 ins. = 1 ft., there
are 6 people in my family)
Significant figures are used to indicate the amount of variationwhich is allowed in a number.
Significant Figures
Closer to the actual value than any other digit.
Significant figures:
3.69 – 3 significant digits.
36.900 – 5 significant digits.
Scientific Notation
3x10^2 (1 significant digit)
3.0x10^2 (2 significant digits)
Rules for Multiplying and Dividing
Number of sig. = the same as the number with the least
number of significant digits.
6.59 x 2.3 = 15 (15.157)
32.65/24=1.4 (24 is not a counting number)
32.65/24=1.36 (24 is a counting number)
Rules for Adding and Subtracting
Result can have no more sig. fig. after the decimal point
than the number with the fewest sig. fig. after the
decimal point.
38.26 – 6 = 32 (6 is not a counting number)
38.2 - 6 = 32.2 (6 is a counting number)
38.26 – 6.1 = 32.2 (rounded from 32.16)
If the last digit >=5 then round up, else round down
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.
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
Difference between accuracy and precision