Marginal and Conditional Researchers looking at the relationship between the type of college attended (public or private) and achievement gather the following data on 3265 people who graduated from college in the same year. The variable “management level” describes their job description 20 years after graduating from college. a. Calculate the marginal distribution of management level in percents. b. Find the conditional distribution of management level for each college type, in percents. c. Sketch the data from part (b) in a segmented bar graph and in a side-by-side bar graph. 182 1756 1327 1769 1496 3265 a. Calculate the marginal distribution of management level in percents. 182 High 5.6% 3265 1756 Medium 53.8% 3265 1327 Low 40.6% 3265 182 1756 1327 1769 1496 3265 b. Find the conditional distribution of management level for each college type, in percents. Public High Medium Low 𝟕𝟓 =4.2 % 𝟏𝟕𝟔𝟗 𝟗𝟔𝟐 = 54.4 % 𝟏𝟕𝟔𝟗 𝟕𝟑𝟐 𝟏𝟕𝟔𝟗 = 41.4 % Private 𝟏𝟎𝟕 𝟏𝟒𝟗𝟔 = 7.2 % 𝟕𝟗𝟒 𝟓𝟗𝟓 = 53.1 % 𝟓𝟗𝟓 𝟏𝟒𝟗𝟔 = 39.8 % Public Private High 4.2 % 7.2 % Medium 54.4 % 53.1 % Low 41.4 % 39.8 % c. Sketch the data from part (b) in a segmented bar graph and in a side-by-side bar graph. Public Private High 4.2 % 7.2 % Medium 54.4 % 53.1 % Low 41.4 % 39.8 % c. Sketch the data from part (b) in a segmented bar graph and in a side-by-side bar graph. 60 High High 40 Low 10 Low Public Private Low Medium Private 20 20 Public 40 30 Private Med Public % Med Private 80 60 50 Public 100 High Below is a graph showing the total number of Oscar nominations for the four films that had PG or PG-13 ratings. What’s wrong with the way the information is presented in this graph? Using similar figures to compare heights exaggerates the differences between frequencies since people (wrongly) tend to compare areas. Class Freq. 20-40 35 40-60 27 60-100 20 100-200 10 200 – 800 28