GradeBuddy AEM 260 1ST EditionLecture 3Previous LectureI. Level of MeasurementII. Cross-Sectional Vs. Time Series DataIII. Methods of Data CollectionIV. Process of Statistical InferenceV. Descriptive Statistics-Organization and DisplayCurrent LectureI. Descriptive Statistics-Organization and DisplayII. Graphical Displays of Frequency DistributionsIII. Summarizing Quantitative DataDescriptive Statistics-Organization and Display- Qualitative data is essentially labeling- The way we summarize qualitative data is by listing frequencies of each item- Relative and Percent Frequencies are the sameo We have both because some people find it easier to read one over the other- Absolute frequencies have the most information o With absolute frequencies one can create relative or percent frequencieso Relative and percent frequencies cannot be used to recreate original datao Absolute frequencies are difficult to compare across groups-which is why we use relative and percent frequenciesGraphical Displays of Frequency Distributions- Bar Chart: graphical depiction of the information in a frequency distribution (for qualitative data only)o Y-axis contains the frequency valueso X-axis has the qualitative variableso There are gaps between the bars to show that the categories are discreteo There cannot be a trend in the bars because there is no orderingo Bar charts can use absolute, relative, or percent, it still forms the same grapho Scale of the graph is very important. If the scale is too large, then it’s too hard to tell the difference- Listen to the data without bias so you can express honestly to everyone else- Horizontal Bar Charts: reverse of a bar charto More useful when looking at different groupso One can make a side-by-side horizontal bar chartso Easier using percent and relative frequenciesGradeBuddy - Pie Chart: circular graphical depiction of the information in a relative frequency distribution (for qualitative data only) the angle for each segment is calculated as:o Degree of angle= 360x(relative frequency)o Relative frequency= x/n- Pareto Chart: a bar chart for which the display of categories are sorted in descending order left to righto Often used in quality controlSummarizing Quantitative Data- Must be treated differently than qualitative datao Has many more possible outcomes- Data Array: listing of the observed values which belong to a data set in either ascending/descending ordero Easier to find the minimum, maximum, mean, median, and mode as well as see if data is more compact ect.- Frequency Distribution Table: a tabular summary showing the relative number of elements in a data set that are in each of several mutually exclusive (non-overlapping) categories (or class)o Steps to determine a class for quantitative data:1. Find the range (r) of the data seta. Largest data value-smallest data value2. Decide on the number of mutually exclusive and collectively exhausted classes (K)a. Usually want between 5 and 15 classesb. Can use Struge’s rule [K=1+3.322x(log n)]i. Usually will have to round up or downc. Can use the sample size square root rule (K= the square root of n)i. Can end up being too many groupsd. Sturge’s rule grows slower than the square root rule as n increasese. You can also use common sense and trial and errori. Trial and error is bad because you can manipulate data to get desired results3. Establish the approximate class width (c.w.)a. C.w. ≈ (Largest value-smallest value)/number of classes desired4. Establish lower and upper class limits and classes5. Record frequencies for each classo Rounding down is not a good idea because it won’t cover all the classeso Rounding up can be bad if one does not disperse the extra units between the end and the