2.4-Statistical Graphs

Transcription

1 2.4-Statistical Graphs Frequency Polygon: A frequency polygon uses line segments connected to points directly above class midpoint values. Example: Given the following frequency table for the pulse rate of females, construct a frequency polygon of the data. Pulse Rate Frequency Solution: Notice that the data point is located at the midpoint of each class. 15 Frequency Polygon

2 Relative Frequency Polygon: A variation of the basic frequency polygon is the relative frequency polygon which uses relative frequencies for the vertical scale. Ogive: Another type of statistical graph called an Ogive involves cumulative frequencies. Ogives are useful for determining the number of values below some particular value. An Ogive uses class boundaries along the horizontal axis and cumulative frequencies along the vertical axis.

3 Example: Given the following frequency table for the pulse rate of females, construct an Ogive of the data. Pulse Rate Frequency Solution: Notice that the data point is located at the midpoint of each class. 60 Ogive Dotplots: A dotplot consists of a graph in which each data value is plotted as a point (or dot) along a scale of values. Dots representing equal values are stacked. Dotplots are easy to create by hand to provide a quick look at the distribution of the data. In the dotplot below there are three values of 60, four values of 64, five values of 68, etc.

4 Example: A manufacturer records the number of errors each work station makes during the week. The data are as follows Construct a dotplot of the data. Solution: Stemplots: A stemplot (or stem-and-leaf plot) represents quantitative data by separating each value into two parts: the stem, and the leaf. A stemplot provides a quick way to sort data which is required for some statistical procedures such as finding a median. Example: The weights of 22 members of the varsity football team are listed below. Solution:

5 Bar Graphs: A bar graph uses bars of equal width to show frequencies of categories of qualitative data. Vertical scale represents frequencies or relative frequencies. Horizontal scale identifies the different categories of qualitative data. A multiple bar graph has two or more sets of bars, and is used to compare two or more data sets. The bar graph below shows the median income of men and woman. Example: The table below from the U.S. National Center for Educational Statistics shows the distribution of undergraduate college student enrollments. Construct a Bar Graph and Pareto Chart for this data. Relative Type of College Frequency Public 2-Year 36% Public 4-Year 40% Private 2-Year 2% Private 4-Year 22% Solution: A bar graph is a type of histogram for qualitative data. That means that the horizontal axis does not have quantitative values. It can be created directly from a frequency or relative frequency data table. 50% 40% 30% 20% 10% Undergraduate Enrollment 0% Public 2-Year Public 4-Year Private 2-Year Private 4-Year

6 Pareto Charts: The Pareto Chart is a type of bar graph but the bars are always in descending orderr according to frequencies. This graph can also be made from the frequency or relative frequency table but the categories must be graphed in a different order The following Pareto Chart depicts undergraduate enrollment at various types of colleges. 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Undergraduate Enrollment Public 4-Year Public 2-Year Private 4-Year Private 2-Year Pie Chart: A graph depicting qualitative data as slices of a circle is a pie chart. The size of the slice is proportional to frequency count. The following Pie Chart depicts the various ways students found employment.

7 Example: The Pie Chart and bar Graph below represent the passenger count for each type of air tour conducted by Westwind Air Service during the month of September, Whichh graphic represents the data in the most useful or eye pleasing way? Solution: It is often a matter of preference as to which graphic is best. You decidee for yourself. Passenger Count Rainbow Bridge Lake Powell Passenger Count Monument Valley Canyonlands Tour Triangle Tour Grand Canyon Tour West Rim Tour Bryce Canyon Flight Grand Canyon Overflight Example: A survey of the 3367 vehicles on the campus of State University yieldedd the following pie chart. Find the number of vans. Round your result to the nearest whole number. Solution: The number of vans is 8% of 3367 which is 269.

8 Scatterplots: A plot of paired (x, y) data with a horizontal x-axis and a vertical y-axis. Scatterplots are used to determine whether there is a relationship between the two variables Example: The following scatterplot represents the amount of garbage vs. household size. Is there an apparent relationship between household size and garbage? Solution: There appears to be a very slight relationship between household size and the amount of garbage. As the household size increases, the amount of garbage is increasing. This relationship would seem to make sense. 6 Garbage vs Household Size

9 Time Series Graph: A time series graph is a graph of time series data which are quantitative data that have been collected at different points in time. Important Points: 1. For small data sets of 20 values or fewer, use a table instead of a graph. 2. A graph of data should make the viewer focus on the true nature of the data, not on other elements, such as eye-catching but distracting design features. 3. Do not distort data, construct a graph to reveal the true nature of the data. 4. Almost all of the ink in a graph should be used for the data, not the other design elements. 5. Don t use screening consisting of features such as slanted lines, dots, cross-hatching, because they create the uncomfortable illusion of movement. 6. Don t use area or volumes for data that are actually one-dimensional in nature. (Don t use drawings of dollar bills to represent budget amounts for different years.) 7. Never publish pie charts, because they waste ink on non-data components, and they lack appropriate scale.