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Graphing Data Unit 2 Sometimes it is easier to identify patterns of a data set by looking at a graph of the frequency distribution. One such graph is a frequency histogram. ◦ A frequency histogram is a bar graph that represents the frequency distribution of a data set. A histogram has the following properties. ◦ 1. The horizontal scale is quantitative and measures the data values 2. The vertical scale measures the frequencies of the classes. 3. Consecutive bars must touch . In a histogram the consecutive bars must touch, must begin and end at class boundaries instead of the class limits. Class boundaries are the numbers that separate classes without forming gaps between them. You can mark the horizontal scale either at the midpoints or at the class boundaries. Graphs of Frequency Distributions Find the Class Boundaries Class Class Boundaries Frequency 7-18 19-30 6.5-18.5 18.5 – 30.5 6 10 31-42 43-54 55-66 67-78 79-90 30.5-42.5 42.5-54.5 54.5-66.5 66.5-78.5 78.5-90.5 13 8 5 6 2 To find the class boundaries, take the distance from the upper limit of the first class and subtract it from the lower limit of the second class. ( 19-18=1) Half this distance is 0.5. So, the lower and upper boundaries of the first class is 6.5 – 18.5 Constructing a Frequency Histogram Interpretation: From either histogram you can see that more than half of the subscribers spent 19 and 54 minutes on the internet during their most recent session. Another way to graph a frequency distribution is to use a frequency polygon. Because the graph should begin and end on the horizontal axis, extend the left side to one class width before the first class midpoint and extend the right side to one class width after the last class midpoint. Other graphs A cumulative frequency graph or ogive is a line graph that displays the cumulative frequency of each class at its upper class boundary. The upper boundaries are marked on the horizontal axis, and the cumulative frequencies are marked on the vertical axis. Step 1: Draw and label the x and y axis. Step 2: Choose a suitable scale for the frequencies or cumulative frequencies, and label it on the y axis. Step 3: Represent the class boundaries for the histogram or ogive, or the midpoint for the frequency polygon, on the x axis. Step 4: Plot the points and then draw the bars or lines. Constructing Statistical Graphs The previous graphs were constructed by using frequencies in terms of raw data. These distributions can be converted to distributions using proportions instead of raw data as frequencies. These types of graphs are called relative frequency graphs. Relative Frequency Graphs