Statistics Unit 2: Organizing Data Ms. Hernandez St. Pius X High School

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 Match graph to data –Appropriate graph for specific data Types –Bar –Pareto Charts –Circle –Time-series –Frequency Distributions –Histograms –Stem and Leaf Plots

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)

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.

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?

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.

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.

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

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

Example 3 on pages From 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

Example 3 on pages From 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, (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

Example 3 on pages From 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

Example 3 on pages From 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

Example 3 on pages From 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

Example 3 on pages From 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

Relative Frequency Tables and Histograms