STAT 200: Week 2 Notes
STAT 200: Week 2 Notes STAT 200
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This 3 page Class Notes was uploaded by Alicia Polcha on Sunday January 24, 2016. The Class Notes belongs to STAT 200 at Pennsylvania State University taught by Prof. Justin Keller in Spring 2016. Since its upload, it has received 15 views. For similar materials see Elementary Statistics in Statistics at Pennsylvania State University.
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Date Created: 01/24/16
Chapter 2, Part One: Frequency Distributions, Histograms, and Related Topics 1. Frequency Distribution: paritions data into classes and assigns each class a frequency a. Frequency Tables: displays information in a frequency distribution, by listing each class along with its frequency b. Constructing a Frequency Table i. Decide on a number of classes between 5 and 15 ii. Calculate the class width 1. (Highest ValueLowest Value) / (# of Classes) a. (# of Classes) What was chosen in step one b. then, increase this value of class width to the next highest whole number. c. NOTICE: Even if it is an exact whole number, you will still increase it to the next highest. i. Example: 1. 6.0 7 iii. Find all lower class limits by starting with the lowest data value and successively adding the class width iv. Find all upper class limits by stopping at the whole number just below the lower limit of the next highest class v. EXAMPLE ( class width = 5 ) 1. Class Width Lower Limit Upper Limit a. 92 96 b. +5 97 101 c. +5 102 106 d. Continue until you reach the “Number of Classes” you need, which was chosen in Step One. vi. To find Frequency: 1. Go row by row through the table of numbers given to find all numbers between specific lower and upper limit. Cross values out each time so you do not recount a number. a. Example: From example above, the first set is from 8286. Count all numbers in the table between these two numbers (8286), this will represent the frequency. 2. Histogram: graphically displays the information in a frequency distribution a. Construction of Histogram i. Add two columns to frequency table for class boundaries 1. Add the title heading “Lower Boundary” and “Upper Boundary” 2. Find boundaries by adding or subtracting 0.5 from the lowers and upper class limits a. Example: For lower boundary, subtract 0.5 from the lower limit. For upper boundary, add 0.5 to the upper limit. b. No data value can ever fall on a boundary because all data in these tables are whole numbers 3. On the horizontal axis of histogram, label the class boundaries 4. Label the vertical axis with Frequencies 5. For each class, draw a bar extending to a height that matches the frequency of that class a. Histogram will look like a bar graph with bars touching from left to right. (no spaces on xaxis) i. Data values on xaxis (boundaries) ii. Frequencies on yaxis b. Does not have to start at the origin, or zero. Must insert the symbol in order to show there is no data to that point in the graph. c. Label frequencies above bars so it is easier to read! b. Relative Frequency: (Frequency/n) i. “ % of the whole “ ii. (Class Frequency/ total of all frequencies) c. Cumulative Frequency: Total of all frequencies at or below this class. d. Ogive: visual display of cumulative frequency, that is often plotted on the same axes as the histogram. Often with separate scale (generate scale on the right side of the histogram i. Looks like a line graph plotted on top of bar graph Chapter 2, Part Two: Bar Graphs, Circle Graphs, and TimeSeries: 1. Bar Graphs: a. Can display qualitative or quantitative data (Biggest difference from histogram) b. Bars can be used to represent: i. Values of a variable ii. Frequency of occurrence iii. Percentage of occurrence c. Bars can be horizontal or vertical d. Bar width and spacing should be uniform e. Pareto Chart: i. A type of Bar Graph ii. Uses bars to represent frequency of event** iii. Arranges bars by decreading frequency** iv. Used for analysis, troubleshooting things that go wrong and find out hwy 1. Example: Widget failure by cause v. Advantage: see biggest causes of failures and compare data to prevent further failures. 2. Circle Graphs (pie charts) a. Show breakdown of population into groups that share common attribute 3. TimeSeries Graph a. Plots the values of a variable measured repeatedly over time b. Time intervals should be uniform c. Labels: i. Time axis (with units) ii. Title iii. Variable axis (with units) Chapter 2, Part Three: 1. Exploratory Data Analysis (EDA): is a field whose goal is to identify patterns and extreme values in data sets without necessarily having an intial question in mind a. Allow data to suggest new ideas or areas of inquiry, without making prior assumptions about what we expect to see 2. Stem and Leaf Display: Technique used in exploratory data analysis to arrange data into groups by size, while simultaneously displaying that visually. a. Constructin of Stem and Leaf Plot i. Divide digits of each data value into two parts between two place values. The left part is the stem, the right is the leaf. ii. Align all stems between the smallest to largest data values in a vertical column to the left of the vertical line. iii. To the right of the ertical line, make a row of all leaves sharing that stem, in increasing order iv. Include a label to show the magnitude of the data, the position of the decimal place and the units. 1. Example: a. 37 3|7 i. ( 3 stem, 7 leaf ) b. 125 12|5 i. ( 12 stem, 5 leaf )
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