Meeting 05 Normal Distribution and Z tables - Ijaz (1).pptx

# Meeting 05 Normal Distribution and Z tables - Ijaz (1).pptx...

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Texas A&M University ENGR 112 – Spring 2018 Foundations of Engineering II Meeting 05 Normal Distribution & Z-tables Please log on to eCampus; we have a RAT and a CFU to start with.

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Agenda Please complete and submit your work on both of the following: RAT – Meeting 05 (password is “ pelletfeeder ”) CFU – Meeting 05
Agenda RAT – Meeting 05 (password is “ pelletfeeder ”) CFU – Meeting 05 A Look-ahead Histograms (Again) Understanding standard normal distribution Understanding how to use a z-table (by hand) Understanding how to do the equivalent z-table calculations in Excel and MATLAB Given a set of population normal-distribution parameters, how to determine the probability of a trial to be within a given range of outcomes

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Measure of Variation for the Population Mean of population Population Variance: Degree of spread using data representing the entire population: Population Standard Deviation : The mean of the residual values is zero – therefore, we find the mean of the squares of the residual values. n i i x n 1 2 2 1 1 1 n i i x n 2 1 1 2 2 1 n i i x n
Measure of Variation for a Sample Sample Variance: Degree of spread: Sample Standard Deviation : Small sample Large sample 2 2 2 1 1 1 1 ( ) or ( ) 1 n n i i i i s x x x x n n 2 s s

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Bins categorize/group data Given the data set [ 1 2 2 3 3 4 5 5 5 5 7 7 8 9 9] Let’s divide the range into five bins How many of the data points (frequency) can be categorized in each bin? 5 5 5 5 4 2 2 8 8 9 9 1-2 3-4 5-6 7-8 9-10 Bins categorizing data - units Frequency of values in bins - counts The mean is the theoretical center value (average) (Central tendency also results in mode and median being at the center) 1 3 3 7 ‘How far is each data point from the theoretical center’ describes variance in the data set?
Consider the following set of Data Image source: - 2009-02-20 Characterizing batches of peanuts coming from farms

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Descriptive Statistics of Major Diameter of a Peanut Crop What do you find interesting about the first three descriptive statistics? What does this tell us about our data? Peanut Crop Major Diameter Statistics Mean 18.13 Median 18.18 Mode 18.19 Variance 4.07 Std Deviation 2.02 Minimum 11.23 Maximum 25.03 25th Percentile 16.75 75th Percentile 19.29 Count 231
Peanut Crop Major Diameter Histogram 0 10 20 30 40 50 60 70 Frequency

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Frequency Distribution of Data
A few terms used in Statistics Trial Getting a data point (or a set of data points) Event Outcome of a trial Probability Measure of the likelihood that an event will occur. 1 Bin is also called Class. Bin size is also called Class Interval 1 (Reference: Wikipedia; visited 02/08/2017)

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0 10 20 30 40 50 60 70 Frequency Probability Histograms can be used to determine the probability of a value falling into a given classification.
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