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