Sec 2.4 Statistical Graphics Key Concepts: Graphs are excellent tools for describing, exploring and comparing data. Describing data: Histogram‐ consider distribution, center, variation, and outliers. Exploring data: Features that reveal some useful and/or interesting characteristic of the data set. Comparing data: construct similar graphs to compare data sets. Definitions: 1. Frequency Polygon uses line segments connected to points located directly above class midpoint values. 2. Relative Frequency Polygon uses relative frequencies (proportions or percentages) for the vertical scale. 2. Ogive is a line graph that depicts cumulative frequencies. 1 Sec 2.4 Statistical Graphics 3. Dotplot consists of graph in which each data value is plotted as a point (or dot) along a scale of values. 4. Stemplot (or stem-and-leaf plot) represents quantitative data by separating each value into two parts: the stem (such as the leftmost digit) and the leaf (such as the rightmost digit). Pulse Rates of Females 5. Bar graph uses bars of equal width to show frequencies of categories of qualitative data. 6. Multiple bar graph has two or more sets of bars, and is used to compare two or more data sets. Median Income of Males and Female 7. Pie Chart: a circle that is divided into sectors that represent categories 2 Sec 2.4 Statistical Graphics 8. Pareto chart is a bar graph for qualitative data, with the added stipulation that the bars are arranged in descending order according to frequencies. 9. Scatterplot is a plot of paired (x, y) quantitative data with a horizontal x-axis and a vertical y-axis. 10. Time-series graph is a graph of time-series data, which are quantitative data that have been collected at different points in time. 3 Sec 2.4 Statistical Graphics 1. Stemplot How to make a stem-and-leaf display 1. Divide the digits of each data value into two parts. The leftmost part is called the stem and the rightmost part is called the leaf (ones digit or decimal place). 2. Align all the stems in a vertical column from smallest to largest. Draw a vertical line to the right of all the stems. 3. Place all the leaves with the same stem in the same row as the stem, and arrange the leaves in increasing order. 4. Use a label to indicate the magnitude of the numbers in the display. We include the decimal position in the label rather than with the stem or leaves. Example 1: Use a stem‐and‐leaf plot to display the data. The data represent the ages of the top 25 wealthiest people in the world. Be sure to indicate the scale. 51 76 67 80 56 73 58 71 78 49 62 84 50 49 87 40 59 47 54 84 61 79 59 52 63 Answer: Interpretation: 2. Dotplot Example 2. Use data from example 1 to construct a dot plot and identify unusual data values 51 76 67 80 56 73 58 71 78 49 62 84 50 49 87 40 59 47 54 84 61 79 59 52 63 Answer: The horizontal axis should include numbers between 40 to 84 (smallest to largest data values) Interpretation: 4 Sec 2.4 Statistical Graphics 3. Pie Chart Example 3. Use a pie chart to display the data. The data represent the number of countries in the United Nation by continent. (Source: United Nations) Continent Number of Relative countries, f frequency North America 23 South America 12 Europe 43 Oceania 14 Africa 53 Asia 47 Total Interpretation: 4. Pareto Chart Example : Use the data from example 3 to construct Pareto Chart (frequency) 5 .