Math 119 Chapter 2 Part 2

The first paragraph introduces the concept of frequency polygons, explaining how they are constructed using line segments connected to points located above class midpoints, representing frequency. The instructor discusses potential discrepancies between the notes and homework due to edition differences and emphasizes the importance of grasping the concepts rather than strictly aligning with the textbook. The summary includes a step-by-step guide on finding class midpoints and plotting them, with an example using specific data points such as 89.5, 109.5, etc., and their corresponding frequencies. The distinction between frequency polygons and smooth curves is highlighted, and the relative frequency polygons are briefly mentioned.

This section delves into ogives, a type of graph that uses class boundaries on the horizontal axis and cumulative frequencies on the vertical axis. The cumulative frequency is explained as the sum of all values within a class interval, including those before it. The instructor provides a step-by-step example, starting with identifying class boundaries and plotting cumulative frequencies, using a smaller marker for visibility. The summary illustrates the process of calculating cumulative frequencies, such as adding 9 to 24 to get 33 at a certain class boundary, and plotting these values to form the ogive graph.

The third paragraph focuses on dot plots, a straightforward graphing method that involves placing dots above a horizontal scale to represent individual observations. The instructor outlines the steps to create a dot plot, including labeling the scale with variable names and values, and placing dots for each observation. An example is given with a range of values from 60 to 130, showing how to place dots for each frequency count. The summary also discusses the limitations of dot plots when dealing with large datasets, suggesting that histograms would be more appropriate in such cases.

The fourth paragraph introduces stem and leaf plots, which are used for graphing quantitative data with a small number of observations. The process involves arranging data in ascending order and separating each value into a stem (all digits except the rightmost) and a leaf (the rightmost digit). The instructor uses an example of scores from a listening test in French, demonstrating how to create a stem and leaf plot and how to interpret it for data shape, center, and spread. The explanation includes determining the median as the 11th value in a set of 21 data points, which is 29 in this case.

This section explains the use of split stem and leaf plots for a more detailed representation of data, especially when regular stem plots are not detailed enough. The method involves writing each stem twice, with the first assigned to lower leaves and the second to higher leaves. An example using the mean density measurements of the Earth is provided, showing how to construct a split stem plot with specific values like 4.1, 4.3, 5.3, etc. The summary discusses the left-skewed nature of the data, the center as the 15th data value (5.5), and the spread from 4.1 to 6.4 grams per centimeter cubed.

The sixth paragraph discusses back-to-back stem plots, which are used to compare two different datasets by sharing the same internal stem and having one set of leaves extend to the left and the other to the right. An example with weights of college students separated by gender is given to illustrate the method. Additionally, the paragraph briefly introduces scatter plots, which will be covered in more depth in later chapters, and mentions their use in representing data to find relationships between two variables.

This section touches on time series and categorical graphs, explaining their use for visualizing data over time and categorical data, respectively. The instructor mentions pie charts for showing percentages and bar charts for representing categories with frequencies or percentages. An example of a bar chart for the average number of babies born each day of the week in 2003 is provided, with a note on the potential reasons for fewer births on weekends, such as doctors avoiding scheduling C-sections or induced labor during their off days.

The final paragraph addresses the issue of misleading graphs, particularly those that do not start at zero on the vertical axis, which can exaggerate differences between categories. The instructor uses an example of a fuel consumption graph comparing the Honda Civic, Chevy Aveo, and Toyota Camry to illustrate how the absence of a zero axis can mislead viewers into perceiving a larger difference in fuel economy than actually exists. The summary contrasts this with a more accurate representation that starts at zero, providing a fair comparison and emphasizing the importance of truthful and clear data presentation.