Frequency Distributions and Statistical Graphs
- A frequency distribution provides a way to organize data.
- A number of classes are created.
- A all classes are the same width
- All classes are disjoint
- The entire range of the data should be covered by the classes.
- Each class has
- A lower class limit (or lower value that fits in the class)
- An upper class limit (or maximum value that fits in the class)
- Begin by setting the class width.
- This will be given in most problems.
- In real life, this is probably the most important parameter as it controls how the data can be perceived.
- Find the minimal data value and that will become the lower class limit for the first class.
- Form other classes
- Add the class width to the lower class limit to form the next lower class limit
- Subtract 1 (or the precision) from the new lower class limit to give the previous upper class limit.
- Continue until a class continuing the maximum data has been found.
- Finally count the number of data items that fit in each class.
- Do #13 page 793
- We might need to adjust the precision if we are not dealing with integer data.
- Do #18 page 793
- The class mark is found by averaging the lower and upper class limits.
- We will use the class mark for the graphs we will draw.
- Compute the class mark for the two exercises.
- A Histogram is a column graph which represents a frequency distribution
- Form the frequency distribution.
- Mark the X axis with the class marks.
- Label the X axis with the item being displayed
- Mark the Y axis with a scale that goes from 0 to the highest frequency.
- Label the Y axis with "Frequency of ", or "Number of "
- Draw a polygon centered on the class mark, the height of the class frequency with a width of one for each class.
- A frequency polygon is constructed the same way, except:
- Draw lines between the frequencies, not polygons.
- Connect the first and last class frequency to the x axis.
- A pie chart or circle graph
- Build the frequency distribution.
- Calculate the percent of the data in each class.
- Calculate the angle of each slice (360*percent)
- Draw the circle graph.
- Stem and leaf displays
- A quick and dirty frequency distribution/histogram
- Select a stem Construct the chart.
- Build the "leaves"
- Do number 28D (at least) page 794