HISTOGRAMS What is the difference between quantitative data

HISTOGRAMS What is the difference between quantitative data and categorical data? 1

HISTOGRAMS Categorical data consists of observations that can be separated into categories. Examples include favorite sport, favorite type of automobile, what state a person was born in, etc. Circle graphs or pie charts are often used to display the data. An example follows. 2

Circle Graphs or Pie Charts A pie chart is often used to plot categorical data when the choices are nonnumeric. 3

HISTOGRAMS Quantitative data consists of observations that have numerical values. Examples include the price of a gallon of gasoline, the ages of your classmates, and the heights of buildings in a city. This data is often displayed in bar graphs or histograms. An example follows. 4

Histograms Histogram ◦ A bar graph plot of the data, with the bars placed adjacent to each other. 5

Histograms Characteristics of data detected by histograms 6

Histograms Characteristics of data detected by histograms 7

Histogram Example Table 2. 8 gives the birth rates (per 1000 population) in each of the 50 states of the United States. Plot these data in a histogram. 8

Histogram Example Solution ◦ Since the data range from a low value of 12. 4 to a high of 21. 9, let us use class intervals of length 1. 5, starting at the value 12. ◦ With these class intervals, we obtain the following frequency table. ◦ A histogram plot of these data is presented as follows. 9

Individual Practice The following data set represents the scores on intelligence quotient (IQ) examinations of 40 sixth-grade students at a particular school: 114, 122, 103, 118, 99, 105, 134, 125, 117, 106, 109, 104, 111, 127, 133, 111, 117, 103, 120, 98, 100, 130, 141, 119, 128, 106, 109, 115, 113, 121, 100, 130, 125, 117, 119, 113, 104, 108, 110, 102 (a) Present this data set in a histogram. Use intervals of 10. (b) Which class interval contains the greatest number of data values? (c) Is there a roughly equal number of data in each class interval? (d) Does the histogram appear to be approximately symmetric? Why? 10