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Statistics Unit 2: Organizing Data

Statistics Unit 2: Organizing Data. Ms. Hernandez St. Pius X High School 2006-2007. Saying it with Pictures. Organizing Data Graphic Summaries Show data Encourage reader focus on data Yet, avoid distorting what data have to say See examples on pg 40 compare/contrast. Basic Graphs.

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Statistics Unit 2: Organizing Data

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  1. Statistics Unit 2:Organizing Data Ms. Hernandez St. Pius X High School 2006-2007

  2. Saying it with Pictures • Organizing Data • Graphic Summaries • Show data • Encourage reader focus on data • Yet, avoid distorting what data have to say • See examples on pg 40 compare/contrast

  3. Basic Graphs • Match graph to data • Appropriate graph for specific data • Types • Bar • Pareto Charts • Circle • Time-series • Frequency Distributions • Histograms • Stem and Leaf Plots

  4. Bar Graphs • Bars are vertical or horizontal • Bars are uniform and evenly spaced • Length of bar represents the value of the variable that is being displayed • Percentage or frequency • Same measurement scale is use for each bar • Title, labels (bar, axis, value)

  5. Examples • Page 42, 43 (good ex) • Page 90 (bad ex) • Compare/contrast the “good” vs “bad” examples of bar graphs on pages 42, 43, and 90. • What kind of data is appropriate for a bar graph? Quantitative or Qualitative data Quantitative Data: Measurement itself is usually displayed. Measurement scale should be consistent. Qualitative Data: Frequency or percentage of occurrence is usually displayed.

  6. Pareto Charts • “Pa-ray-toe” Charts • Specific type of bar graph • Bar height represents frequency of event • Bar are arranged from left to right – decreasing height • Example on page 44 What kind of data is appropriate for a Pareto Chart? Identify the frequency of events or categories in decreasing order of frequency of occurrence Say what?

  7. Circle Graphs • AKA “pie” chart • Percentages • Examples on pg 45, 98 • What kind of data is appropriate for a circle graph? Display how a TOTAL is dispersed into several categories. Mostly for Qualitative data, or anything where the percentage of occurrence makes sense. 10 or less categories is best.

  8. Time-Series Graph • Data are plotted in order of occurrence at regular intervals over a period of time • Measure same thing over a period of time at specific (hopefully) periods of time • Distance jogged in 30 minutes (pg 47) • Stock price for Coca-Cola (pg 52) • Stock price history for Mickey D’s (pg 52) What kind of data is appropriate for a time-series graph? Display how data change over a period of time. Keep consistent units of time.

  9. Frequency Distributions • Anything that shows the distribution of data into “classes” or intervals. • Frequency table • Frequency histogram • Relative frequency table • Relative frequency histogram

  10. Classes or Intervals • First need a frequency table (pg 53) • The frequency table organizes data • In the frequency table WE make distinct data intervals that cover all the data • These intervals are called “classes” • The classes are disjoint • Each data value will fall in one and only one interval or class • Corresponds to one bar in a histogram

  11. Example 3 on pages 53-56From a Frequency Table to a Histogram • List all data recorded • Make a Frequency Table: • Think about how many classes you will use • Too few and you will lose the variability in the data (only see the tree in the forest) • Too many and you many not really see a summary (see all trees in the forest but not the forest) • Next, determine the CLASS WIDTH • Page 54 • Next, determine the CLASS RANGE (aka Class Limits) • Page 54 • Next, calculate the CLASS MIDPOINT • Page 55 • Finally, you are now ready to construct your histogram

  12. Example 3 on pages 53-56From a Frequency Table to a Histogram • 6 classes (we already determined this … well its from ex 3) • Next, determine the CLASS WIDTH (pg 54) • Largest data value minus the smallest data value divided by the numer of class you decided to use • Round up to the nearest whole number • 7.7 is rounded up to 8 • So now we have 6 classes and with width of 8 • The widths correspond to data values • Data values from 1-8, 9-16, 17-24, 25-32, 33-40, 41-48 (bottom of pg 54) • Next, determine the CLASS RANGE (aka Class Limits) • Page 54 • Next, calculate the CLASS MIDPOINT • Page 55 • Finally, you are now ready to construct your histogram

  13. Example 3 on pages 53-56From a Frequency Table to a Histogram • 6 CLASSES • CLASS WIDTH is 8 • Next, determine the CLASS RANGE (aka Class Limits , pg 54) • Limits are the smallest (lower limit) and the largest (upper limit) data value that can be in any one class • In the first class, the width is 1 to 8 • lowest value is 0.5 (less than 1) and the highest value is (8.5) • In the second class, the width is 9-16 • lowest value is 8.5 (less than 1) and the highest value is (16.5) • And so on … see bottom of page 54 • Next, calculate the CLASS MIDPOINT • Page 55 • Finally, you are now ready to construct your histogram

  14. Example 3 on pages 53-56From a Frequency Table to a Histogram • 6 CLASSES • CLASS WIDTH is 8 • CLASS RANGE (aka Class Limits , pg 54) • Next, calculate the CLASS MIDPOINT (pg 55) • Midpoint is usually used to represent the data in each class • It’s the “class representative” • Lower limit minus the upper limit and divide by two • Calculated for each class • Finally, you are now ready to construct your histogram

  15. Example 3 on pages 53-56From a Frequency Table to a Histogram • 6 CLASSES • CLASS WIDTH is 8 • CLASS RANGE (aka Class Limits , pg 54) • CLASS MIDPOINT (pg 55) • Finally, you are now ready to construct your histogram • But wait! We need CLASS BOUNDARIES!!! • The bars touch in a histogram • Upper class boundary • Add 0.5 unit to upper class limit • Lower class boundary • Add 0.5 unit to lower class limit

  16. Example 3 on pages 53-56From a Frequency Table to a Histogram • Make a Frequency Table • Example is on page 54 • Procedure is summarized on page 56 • 6 CLASSES • CLASS WIDTH is 8 • CLASS RANGE (aka Class Limits , pg 54) • CLASS MIDPOINT (pg 55) • CLASS BOUNDARIES (pg 55-56) • Draw Histogram (pg 56) • Procedure is summarized on page 56

  17. Relative Frequency Tables and Histograms

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