An Example of a Class Frequency Histogram. An Example of a Class Frequency Table. Freq

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1 Section A: uency Histograms for Discrete Quantitative Data The data in a uency Table can be made more visual by creating a graph of the classes and their frequencies. One type of graph used for this purpose is called a uency Histogram (bar graph). A histogram is a graph made up of rectangles placed on an x and y axis. Each rectangle represents one class in the uency Table. An Example of a uency Table 6 3 An Example of a uency Histogram Number of Units Notice that the numbers on the horizontal axis are not the class limits from the table. Horizontal Scale The base of each rectangle is placed on the x axis. The rectangles are placed next to each other with no gaps between them. (not class limits) are used to represent the location on the horizontal line where each rectangle representing that class starts and ends. The left and right sides of the rectangle have numerical values on the x axis that are the class for each class. The class boundary for each rectangle is. below the lower class limit and. above the upper class limit of the class that the rectangle represents. Vertical Scale The vertical scale on the the y axis represents the possible class frequencies. The height of each rectangle is found using the vertical scale on the y axis. The height of the rectangle represents the frequency for the class the rectangle represents. Section A Lecture Page of 6 0 Eitel

2 Using the Limits to locate the rectangles on the x axis will leave gaps between the rectangles If we tried to make a uency Histogram from the uency Table below the first rectangle, representing the first class, would start at and end at 3. The next rectangle, representing the second class 6, would start at and end at 6. The next rectangle, representing the third class, would start at 7 and end at 9. There would be a gap between the rectangles when we place them on the x axis. Because the values of x in the table are discrete numbers there is a gap between the upper class limit of one class and the lower class limit of the next class. Second Third 6 First gap gap Our definition of a uency Histogram requires that the numbers that will represent each class be placed on the horizontal x axis in such a way that there is no gap between the numbers that will represent each class. The rectangles must be drawn next to each other with no gaps between them. Simply moving the rectangles together on the x axis and putting the class limits at the ends of each rectangle will not work First Second Third The rectangle that represents the first class 3 ends at 3, and the rectangle that represents the second class 7 starts at. If the 3 rectangle must end at 3 and the 6 rectangle must start at and they must have no gap between them then we have a problem. The x value for the right side of the first rectangle is 3 and it would be at the same location as the left end of the second rectangle that starts at. The same problem happens where the 6 bar ends and the 7 9 bar starts. Section A Lecture Page of 6 0 Eitel

3 The use of class will solve this problem. Boundaries of units Limits 6 Boundaries: A class are numbers halfway between class limits that are used to separate the classes in such a way that the class width stays the same, the class values stay the same but allows each class to be represented by numbers that do not have a gap between them. The value of a class boundary is a number that is half way between the upper class limit of one class and the lower class limit of the next class. Another way of stating this is to say each class boundary is in the center of the gap between the class limits. For whole numbers The lower class boundary is. less than each lower class limit and the upper class boundary is. more than each upper class limit The class has class of. 3.. less than and. more than 3 The 6 class has class of less than and. more than 6 The class has class of less than 7 and. more than 9 The Boundaries and Limits for a represent the same range of discrete numbers but there is no gap between consecutive class The class. 3. contains,, 3 The class contains,, 3 The class contains,, 6 The class contains,, 6 The class contains 7,, 9 The class contains 7,, 9 Section A Lecture Page 3 of 6 0 Eitel

4 Example : Finding Boundaries Miles driven Miles driven The class has class. less than and. more than. to. The class has class. less than and. more than. to. The class 9 has class. less than 9 and. more than. to. The class 3 6 has class. less than 3 and. more than 6. to 6. The class 7 0 has class. less than 7 and. more than 0 6. to 0. Example : Finding Boundaries with a lower class limit of 0 Age of child Age of child 0. to The class 0 has class. less than 0 and. more than. to. The class 3 has class. less than 3 and. more than. to. The class 6 has class. less than 6 and. more than. to. The class 9 has class. less than 9 and. more than. to. Note:. less than 0 is. Section A Lecture Page of 6 0 Eitel

5 Using Boundaries to graph a uency Histogram Example Boundaries Label each axis Number of Units The y axis is labeled in all uency Histograms. The x axis is labeled based on the description of the data in the x column. This table represents the Number of Units. Place a scale on the horizontal and vertical axis. The scale for the horizontal x axis will be the class. The scale of the vertical y axis will be based on the numbers in the frequency. column. Multiples of, or 0 are common. Place the rectangles on the x axis using the class and frequencies The First Rectangle starts at. on the x axis and ends at 3. with a height of. The Second Rectangle starts at 3. on the x axis and ends at 6. with a height of. The Third Rectangle starts at 6. on the x axis and ends at 9. with a height of. Section A Lecture Page of 6 0 Eitel

6 Example : uency Histogram with a lower Boundary of.. to. Age of child in years 0 freq Age of Child in years Note: The. is not placed on the left side of the y axis. It is placed to the right of the y axis. Label each axis The y axis is labeled in all uency Histograms. The x axis is labeled based on the description of the data in the x column. This table represents the Age of child in years. Place a scale on the horizontal and vertical axis. The scale for the horizontal x axis will be the class. The scale of the vertical y axis will be based on the numbers in the frequency. column. Multiples of are used here. Put the rectangles on the graph using the class and frequencies The First Rectangle starts at. on the x axis and ends at. with a height of. Note: The. is not placed on the left side of the y axis. It is placed to the right of the y axis. The Second Rectangle starts at. on the x axis and ends at. with a height of. The Third Rectangle starts at. on the x axis and ends at. with a height of. The Fourth Rectangle starts at. on the x axis and ends at. with a height of 6. Section A Lecture Page 6 of 6 0 Eitel