2.2 Frequency Distributions and Histograms Histograms are bar graphs in which a. The bars have the same width and _______________________ b. The width of the bar represents a_____________________ value, rather than a _____________________________ c. The height of each bar represents a _____________________________ Class Width 1. Compute (Largest data value-­‐Smallest Data Value)/Desired number of classes 2. Usually use between 5 and 15 classes. (The Problem will tell you) 3. Always round your class width UP to the next whole number. Class Boundaries-­‐ These are the actual DECIMALS that create the boundary of each class Class Midpoint= (Lower Class limit + Upper Class Limit)/2 This is often used as a representative value for the whole class. We will use it later in some calculations Relative Frequency = Frequency of a given class/ Total number of data points To make a Frequency Table 1. Determine the class width 2. Create the distinct classes. The lowest data value is the first lower class limit. Adding the class width to the will get THE LOWER CLASS LIMIT OF THE NEXT CLASS 3. Tally the data into classes. This will get class frequency 4. Compute the midpoint for each class 5. Determine class boundaries. (Decimals that will be actual border of classes One way commuting Distances in Miles for 60 workers in Downtown Dallas 13 47 10 3 16 20 17 40 4 2 7 25 8 21 19 15 3 17 14 6 12 45 1 8 4 16 11 18 23 12 6 2 14 13 7 15 46 12 9 18 34 13 41 28 36 17 24 27 29 9 14 26 10 24 37 31 8 16 12 16 Create a Frequency Table of the Dallas commuting distances with 6 classes. Class Width= Class Class Tally Frequency Class Relative Limits boundaries Midpoint Frequency Create a Histogram of the above data Create a Relative Frequency Histogram (Uses relative frequency as bar height instead of actual tally Create a Frequency Polygon of the above data (use points. Classmidpoint is x, frequency is the y. Plot the points and connect the dots) Skewness