Transcript Descriptive Statistics

Descriptive Statistics
A Short Course in Statistics
Descriptive Statistics
Consists of the
collection,
organization,
summarization,
and presentation of
data.
Often with charts
and graphs.
90
80
70
60
50
40
30
20
10
0
East
West
North
1st
Qtr
3rd
Qtr
Collecting Data
If you can collect
data from
everyone or
everything in
your target of
interest you have
a POPULATION.
The population is
the whole entire
group of interest
Collecting Data
Usually it is
IMPOSSIBLE to
collect every piece
of data. In this case
you have to use a
SAMPLE.
The sample is just
part of the whole
group of interest
After Collecting the Data
Now it is time to do some calculations
and make some graphs!
We will start with determining some
basic measures of central tendency.
Measures of central tendency
measure the center of data.
We will learn to determine Mean,
Median and Mode
Mean
When you usually think of a "middle" score they
often think of what is known as the arithmetic
mean or just mean, for short.
This is what most people also refer to as the
"average" of a set of scores.
I call the Mean the mathematical middle.
You probably already know how to calculate the
mean for a simple list of numbers.
Add all the numbers and then divide by the
number of numbers you have, remember doing
this before?
Let’s Calculate the Mean
The following is a list of
Elliott’s test score from his
math course.
Test 1
Test 2
Test 3
Test 4
68
72
90
86
Now add the numbers
together
68+72+90+86 = 316
Now divide 316 by 4 (the
number of numbers) = 79
79 is the Mean for Elliott’s Math
Scores
Try Your Own Problem #1
Matt’s test scores are as
follows:
Test 1
90
Test 2
88
Test 3
97
Test 4
80
Test 5
70
What was the Mean of Matt’s
test scores?
Let’s take a look.
Median
The median is the number at which half your data
pieces are more than that number and half are less
than that number.
The median cuts the data set in half.
To calculate the mean the data list must be in
numerical order, either smallest to largest or largest to
smallest.
Generally, the median provides a better measure of
location than the mean when there are some extremely
large or small observations that skew the data. For this
reason, median income is used as the measure of
location for the U.S. household's income.
Let’s Find the Median
The following list is the
attendance in my classes on
Tuesday
23, 20,16, 30, 8
First put the list in numerical
order.
8, 16, 20, 23, 30
Position of the median can be
determined by using the
formula
n 1
2
Look for the number that is in
the 3rd position.
The 20 is the Median of this
data set.
Try your own problem #2
Data List
23, 24, 3, 26, 2, 9, 13, 6
Ordered List
2, 3, 6, 9, 13, 23, 24, 26
Find the position
(8+1)/2= 4.5th
Look for the 4.5th number.
Since the 4.5th does not exist,
find the 4th and the 5th and find
the mean of the two numbers.
What’s the Median?
Let’s Take a Look!
Mode
The mode is the most "typical" value
The Mode it is the most repeated value in the data
set.
There might be no mode in a data set, this
happens when all numbers only appear once .
There may be more than one mode, this happens
when more than one data value appears many
times.
If there is more than one mode, all values must
appear in the list the same number of times.
The Mode is most frequently used when
describing qualitative data like religious preference
or eye color.
Let’s Determine the Mode
Your data list does not need to
be in order, but ordering the
list might make it easier to find
the Mode.
Try your own problem #3
2,2,3,5,6,7,7,7,8,9
Which number occurs the
most often in this list?
The 7, so 7 is the Mode of
this set.
Start by ordering the list
2,2,2,3,4,5,7,7,7,8,9
This list has two modes,
both the 2 and the 7 are
the modes.
Which data value appears the
most?
2, 5, 7, 8, 7, 6, 9, 4, 6, 8, 2, 3,
1, 4, 5, 6
(Just to help you out a little)
1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7,
7, 8, 8, 9
Let’s Take a Look!
End of the Lesson
You have reached the end of our first
lesson on descriptive statistics.
You should be able to figure mean,
median and mode for an ungrouped
list of data.
Stop in again for a second lesson,
Making Graphs with Data, coming
soon.
Thanks, Cindy
Answers for Try Your Own
Problems
#1 Matt’s Mean is 85.
#2 The Median is 11.
#3 The Mode is 6.
Return to lesson
Return to lesson
Return to lesson