1. MAT 135 Introductory Statistics and Data Analysis Adjunct Instructor
Kenneth R. Martin
Lecture 3
September 14, 2016
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2. Confidential - Kenneth R. Martin
Agenda
Housekeeping
Readings
Collect HW #2
Review HW #2
Chapter 1, 14, 10, & 2
Quiz #1
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3. Confidential - Kenneth R. Martin
Housekeeping
Read, Chapter 1.1 – 1.4
Read, Chapter 14.1 – 14.2
Read, Chapter 10.1
Read, Chapter 2
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4. Confidential - Kenneth R. Martin
Housekeeping
Collect HW #2
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5. Confidential - Kenneth R. Martin
Housekeeping
Review HW #2
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6. Confidential - Kenneth R. Martin
Housekeeping
Quiz #1
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7. Confidential - Kenneth R. Martin
Review
What have we learned so far ?
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8. Statistics – Application to Research
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9. Confidential - Kenneth R. Martin
Statistics
Why collect samples ?
Often impractical to collect all the data from the entire population (i.e. U.S. census).
Some test methods are destructive – we wouldn’t have any products or services left to ship to a customer!
Too expensive to sample the entire population.
Don’t have to collect 100% of the population ! We can use inferential statistics to make sound conclusions about the population.
Population and Sample
Sampling
Scheme
POPULATION
SAMPLE
Measure
Data!
Use data from the SAMPLE to make conclusions about the POPULATION
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10. Confidential - Kenneth R. Martin
Summarizing Data
Data
The experiment was performed and the data was collected, now what ?
We have the raw data … is it useable ?
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Summarizing Data
We will “describe” the data either:
Numerically (analytically as single values);
Graphically (tables, graphs, charts, etc.);
Both.
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Summarizing Data
Data
Raw Data: represents a listing of all the observed values
Frequency Distribution: represents a lumping together of the observed values into “intervals” (classes), where the frequency of each score can fall into any given interval.
These “Intervals” can be either quantitative or qualitative in nature.
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Summarizing Data
Frequency
A frequency is the number of times or how often a category, score, or range of scores occurs
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Summarizing Data
Frequency Distribution (ungrouped)
When the data set or its range is small
A summarization display of how the data points (observations) occur in a data set.
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15. Confidential - Kenneth R. Martin
Summarizing Data
Frequency Distribution / Histogram
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Summarizing Data
Frequency Distribution (ungrouped)
Column Chart from Excel
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17. Confidential - Kenneth R. Martin
Summarizing Data
Frequency Distribution (ungrouped)
Column Chart from Minitab
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18. Confidential - Kenneth R. Martin
Summarizing Data
Frequency Distribution (ungrouped)
Dot Plot from Minitab
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Summarizing Data
Frequency Distribution (categorical)
A summarization display for data that can be placed in specified categories.
Data can be from categorical / nominal or ordinal level data.
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Summarizing Data
Frequency Distribution (categorical)
Make a Table for the data.
Tally up the frequencies of categories.
Find the percentage of each class / category:
% = (f / n)*100.
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21. Confidential - Kenneth R. Martin
Summarizing Data
Frequency Distribution (categorical)
Column Chart from Excel
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22. Confidential - Kenneth R. Martin
Summarizing Data
Frequency Distribution (categorical)
Column Chart from Minitab
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23. Confidential - Kenneth R. Martin
Summarizing Data
Frequency Distribution (categorical)
Dot Plot from Minitab
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24. Confidential - Kenneth R. Martin
Summarizing Data
Frequency Distribution (grouped)
A summarization display of a larger range of data and how the data points (observations) occur within a “interval / class” of observed values or groups of observed values.
Interval (Bin) / Class Width: range of possible values of each interval.
Open Interval: an interval with no defined upper or lower boundary
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25. Confidential - Kenneth R. Martin
Summarizing Data
Frequency Distribution (grouped)
Lower Boundary / class limit: the smallest possible value in each interval / class of a frequency distribution
Upper Boundary / class limit : the largest possible value in each interval / class of a frequency distribution
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Summarizing Data
Frequency Distribution (grouped)
Rules / Guidelines:
General rule is 5-20 “bins” / classes.
Bins must be mutually exclusive.
Bins must be continuous.
Bins / classes must be exhaustive of data.
Bins must be equal width, except for open-ended bins.
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27. Confidential - Kenneth R. Martin
Summarizing Data
Frequency Distribution (grouped)
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28. Confidential - Kenneth R. Martin
Summarizing Data
Frequency Distribution (grouped)
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Summarizing Data
Frequency Distribution (grouped)
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Summarizing Data
Frequency Distribution (grouped)
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Summarizing Data
Relative Frequency Distribution: summary display that distributes the proportion of values in each interval
Cumulative Frequency Distribution: summary display that distributes the sum of frequencies across a series of intervals
Relative Cumulative Frequency Distribution: summary display that distributes the sum of relative frequencies across the intervals
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Summarizing Data
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Summarizing Data
Histogram
Displays the distribution of measurement (continuous) or discrete data into a bar graph form, for interpretation and presentation.
Maps data, categorizes and counts the number of data points into “bins” (bars)
Bins (on x-axis) are adjacent and non-overlapping and are displayed as the same width
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Summarizing Data
Histogram (from Six Sigma)
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Summarizing Data
Histogram
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Summarizing Data
Histogram
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37. Confidential - Kenneth R. Martin
Summarizing Data
Frequency Distribution & Histogram
Used to analyze data, their associated distributions and to solve problems
Reveals Central Tendency, Variation of data spread & Capability
Reveals if the data is skewed from center (shape)
Reveals the # of modes of data (humps), and any gaps of data
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Summarizing Data
Histogram, steps of construction
Collect and present all data.
Count the total number of data points, n.
Determine the range, R, of the entire data set.
Establish the number of bins, K, from n.
Charts available to refer, typically 5-20 bins
Determine the bin width, W.
W = R / K
Make sure W has 1 more decimal point than in data set
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39. Confidential - Kenneth R. Martin
Summarizing Data
Histogram, steps of construction
Determine the bin boundaries (end points of bins)
Easiest to start with lowest # in data set and add bin width
Construct a frequency table with bin size, bin midpoint, and frequency count of data in each bin.
“Draw” the histogram. The histogram is nothing more than a visual frequency table.
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Summarizing Data
Process aim = 9.0 minutes
Spec = + / minutes
n = 125
R = 1.7
K = 10
W = 1.7 / 10 = 0.17
Round up to 0.20
Assure 1 + decimal point
First bin
Min value = 9.0 (+0.20 width)
(all data <9.2)
Histogram
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41. Confidential - Kenneth R. Martin
Summarizing Data
Frequency Distribution & Histogram
Construct a frequency table and a histogram.
First bin
Min = 9.0 (+0.20)
(all data <9.2)
Second bin
data
Etc.
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42. Confidential - Kenneth R. Martin
Summarizing Data
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Summarizing Data
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44. Confidential - Kenneth R. Martin
Summarizing Data
Histogram
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