Chapter 8 – Basic Statistics

8.1 – Introduction to Basic Statistics

What Basic Statistics Is and Why It Is Important? Statistics is the branch of mathematics that deals with ways of handling large quantities of information. The goal is to make this information easier to interpret. Averages are what most people use to summarize large quantities of data. There are three types of averages: The mean, median, and mode.

What Basic Statistics Is and Why It Is Important? The arithmetic mean, or just mean, is what most people call the average. It is the sum of the numbers divided by the total number of numbers. If a set of numbers arranged in a numerical order, the median of the numbers is the number in the middle. If there are two numbers in the middle, the median is the mean of the two middle numbers. The mode of a set of numbers is the number (or numbers) occurring most frequently in the set. The range of a set of numbers is the difference between the largest and the smallest number in the set. It is not an average.

Examples Determine the mean, median, mode, and range of each set of data. 1. 2, 9, 1, 7, , 7.3, 2.5, 2.8, 3.7,

Example A weighted average is used when some numbers in a set count more heavily than others. Computing your GPA is an example of this. Example: Last semester, a student’s grades were as follows. Compute the student’s GPA for the semester. CourseCreditsGradeGrade Equivalent English4B3 Mathematics4A4 Art3B3 Science3C2

8.2 – Tables and Graphs

What Tables and Graphs Are and Why They Are Important A table is a rectangular display of data. A graph is a picture or diagram of the data. Tables and graphs are efficient ways to summarize data.

Tables A table is a rectangular display of data. A graph is a picture or diagram of the data. A table consists of rows and columns. Rows run horizontally, and columns run vertically.

Example: a. In what room does Math 011, section 091 meet? b. What time does Math 051, section 711 meet? Table

Pictographs Pictographs are a kind of graph in which images are used to represent and to compare quantities. A key is given to explain what each image represents. Example: About how many a associate’s degrees were awarded?

On a bar graph, quantities are represented by thick, parallel rectangles called bars. The length of each bar is proportional to the quantity that it represents. Bar Graphs Example: What was the approximate net income of the company in the year 2002?

A histogram is a graph of the frequency table. In a histogram, adjacent bars touch. For each bar, the width represents the class interval, and the height stands for the corresponding class frequency. Histograms Example: a. How many students scored between 60 and 69? b. In which two intervals did only two students score?

Line Graph On a line graph, quantities are represented as points connected by straight-line segments. The height of any point on a line is read against the vertical axis. Example: In what year did the population number reach about 12 million?

Circle Graphs Circle Graphs are commonly used to show how a whole amount - say, an entire budget or population - is broken into its parts. Example: What fraction of the households own cats?