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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, 9
2. 3.7, 7.3, 2.5, 2.8, 3.7, 9.2
1 5 1 1 5
3. 2 , 1 , 3 , 2 ,1 ,4
3 6 2 3 6
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.
Course
Credits
Grade
Grade
Equivalent
English
4
B
3
Mathematics
4
A
4
Art
3
B
3
Science
3
C
2
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.
Table
Example:
a. In what room does Math 011, section 091 meet?
b. What time does Math 051, section 711 meet?
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?
Bar Graphs
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.
Example: What was the
approximate net income of
the company in the year
2002?
Histograms
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.
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?