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Descriptive and Inferential Statistics

- Descriptive statistics Mathematical methods

(such as mean, median, standard deviation) that

summarize and interpret some of the properties of

a set of data (sample) but do not infer the

properties of the population from which the

sample was drawn. - Mathematical methods (such as hypothesis

development) that employ probability theory for

deducing (inferring) the properties of a

population from the analysis of the properties of

a set of data (sample) drawn from it.

Did it happen by chance?

- How do you know if something caused or correlates

with something else? - The appropriate Statistic will tell you
- If there is a difference from some expected value
- If the difference is statistically significant or

merely due to random chance

Descriptive Statistics

- Types of descriptive statistics
- Calculation for interval data

Types of descriptive statistics

- Statistic is a quantitative index that describes

performance of a sample or samples - Parameter is a quantitative index describing the

performance of a population - Measures of central tendency are used to

determine the typical or average value among a

group of values - Measures of variability indicate how spread out

the values are

Graphing data

- Provides a quick view of the what your data is

telling you. - There are various types of graphs which are used

in statistics including bar graphs, histograms,

scatter plots, pie charts, frequency polygons etc.

Example group of test scores

Frequency Polygon and Pie Chart

Sample Bar Graph

Sample Histogram

Sample Scatter Plot

Frequency Distributions

Frequency distributions are like frequency

polygons however, instead of straight lines, a

frequency distribution uses a smooth curve to

connect the points and, similar to a graph, is

plotted on two axes.

J Shaped Curve

Bimodal Curve with Two Peaks

Positively Skewed Bell Curve

Negatively Skewed Bell Curve

Symmetric Bell Curve/Normal Distribution

What is the Normal Distribution ?

- Where did it come from and why is it so special?
- As shown by Galton (19th century guy), just

about anything you measure turns out to be

normally distributed, at least approximately so. - That is, usually most of the observations cluster

around the mean, with progressively fewer

observations out towards the extremes

Sample Histogram

Just about any histogram can be converted into a

line graph

Which can be used to plot a normal distribution

But how do we get from the normal to the standard

normal?

Measures of central tendency

- Mean arithmetic average of a set of values and

most frequently used measure of central tendency - Median- midpoint of values if they are ordered

from high to low - Mode value that occurs most frequently

Mean, Median and Mode

- Sample Numbers
- 7 26 54 82 32 26 51
- Find the mean, median and mode

Mean

- Finding the Mean X
- Total up the numbers
- Divide the total by the n (number of values)

Mean

- Finding the Mean X
- Total up the numbers (287)
- Divide the total by n (number of values) (287 /

7 39.71)

Median

- Finding the Median
- Swerve the car to the left till you hit something

in the middle of the road - The median is the middle value when numbers are

arranged in order - Arrange numbers from highest to lowest
- Find the middle number (odd number of values)
- 7 26 26 32 51 54 82

Median

- Median trick question
- Find the median now!
- 7 26 54 82 32 26 51 36

Mean, Median and Mode

- 7 26 26 32 36 51 54 82

Split the Difference Between the Two

middle numbers

Median is 34

Mode

- The mode is the value that occurs most frequently
- Arranging the numbers in order helps here
- 7 26 26 32 51 54 82

Mode

- What is this called?
- 7 26 26 32 51 51 54 82

Answer

Bimodal!

Measures of variability

- Range Difference between the highest and lowest

values (high value -low value range) - Variance S2
- Standard Deviation S
- variation of values about the mean

Measures of variation range

- Range highest value-lowest value
- Bank waiting time values
- Values of 4, 7, 7 the range is 7-4 or 3
- With values of 1, 3, 14, the range is 14-1 or 13

Other key measures of variation

- S2 Variance
- S Standard Deviation

(Triloa, Elementary Statistics, 9th Ed, 2004)

Measures of variation standard deviation

x

6 6 6

Measures of variation variance

x

6 6 6

The Z statistic will allow you to standardize a

normal distribution

Lets compare some of the great running backs of

NFL history

Lets compute z-scores..

To derive the Stardard Normal Curve

Bringing us back to the concept of Six Sigma

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