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STAT 200: Week 2 Notes

by: Alicia Polcha

STAT 200: Week 2 Notes STAT 200

Alicia Polcha
Penn State
GPA 4.0

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These notes will cover the entire chapter two, which was covered the week of January 19, 2016. These notes include information on: -Frequency Distribution -Histograms -Relative and Cumulativ...
Elementary Statistics
Prof. Justin Keller
Class Notes
Math, Statistics, stat, Business Math, elementary statistics, frequency distribution, Graphs, analysis, plots
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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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