3. Intro to Statistics
Statistics is the science that deals with the
collection and summarization of data.
Methods of stat analysis allow us to make
conclusions about a population based on
sampling.
Statistics is more a field of Communications,
than one of Mathematics!
4. Intro to Statistics
1. Organize Data
2. Display Data
3. Identify the “averages” of the data
4. Identify the “spread” of the data
5. Make conclusions
5.
6.
7.
8.
9.
10.
11. Obtaining Data
• Want to represent a Population
• Collect data from a Sample
–Should be a Random Sample to be
a fair representation of the
population
12. Displaying Qualitative data with
Frequency Table
FREQUENCY TABLE A grouping of qualitative data into
mutually exclusive classes showing the number of
observations in each class.
14. Displaying quantitative data with
Frequency Distribution
A FrequencyFREQUENCY DISTRIBUTION A grouping of data into
mutually exclusive classes showing the number of
observations in each class.
Classes:
This
Frequency
Distribution
has 7 classes
15. Displaying quantitative date with
Frequency Distribution
Class width: The class
width is obtained by
subtracting the lower limit
of a class from the lower
limit of the next class.
Class frequency: The
number of observations in
each class.
Class midpoint: A point that
divides a class into two
equal parts. This is the
average of the upper and
lower class limits.
16. Constructing a Frequency Table
• Step 1: Decide on the number of classes. (if not already given)
A useful recipe to determine the number of classes (k) is the
“2 to the k rule.” such that
2k > n
There were 80 vehicles sold. So n = 80. If we try k=6, which
means we would use 6 classes, then 26=64, somewhat less than
80.
Hence, 6 is not enough classes. If we let k = 7, then 27 128,
which is greater than 80. So the recommended number of classes
is 7.
17. Constructing a Frequency Table
Step 2: Determine the class interval or width.
The formula is:
where k is the number of classes.
($35,925 - $15,546)/7 = $2,911
Round up to some convenient number, such as a
multiple of 10 or 100. Use a class width of $3,000
k
ClassWidth
minmax
19. 23 22 38 25 11 16
15 26 23 24 37 18
21 36 36 28 18 9
39 17 27 24 10 32
24 27 22 24 28 39
There are 30 Data Items, so n = 30
Where each can be called
So,
“21”, “37”, etc. are Data Values
ix
254 x
20. Organizing Data
• Frequency Distribution Table
– Organize data into Classes
• Usually between 5 - 15
– Each class must have the same Class Width
Class width* =
Max data value – Min data value
Number of classes
*Round up to next highest integer
21. Organizing Data
Let’s make a Freq. Dist. Table with 7 classes to organize
the tuition data…Need Class Width!
28.4
7
939
*
CW
So, each class will have a class width of 5!
22. Organizing Data
Note: Class width is not (9 – 5)!!!
It is the distance between the lower
limit of each class.
Make
this
column
first!
23. Displaying Data
1. An accounting firm selected 24 complex tax returns prepared by a certain tax preparer. The number of
errors per return were as follows. Group the data into 5 classes, and make a frequency table and
histogram/ polygon to represent the data.
Your Class Width =
8 12 0 6 10 8 0 14
8 12 14 16 4 14 7 11
9 12 7 15 11 21 22 19
Create frequency table
24. Displaying Data
• Frequency Histogram (bar graph)
–Each class is its own “bar”
• No spaces between classes (bars)
–Must label each axis (classes vs. frequency)
–Use straightedge to make lines
26. Displaying Data
• Frequency Polygon (line graph)
–Connects the midpoints of the top of each
class.
–Then connect to ground on each side
–Use straightedge to make lines
29. Displaying Data
1. An accounting firm selected 24 complex tax returns prepared by a certain tax preparer. The number of
errors per return were as follows. Group the data into 5 classes, and make a frequency table and
histogram/ polygon to represent the data.
Your Class Width =
8 12 0 6 10 8 0 14
8 12 14 16 4 14 7 11
9 12 7 15 11 21 22 19
Create frequency
histogram/polygon
30. Displaying Data
From worksheet:
2. The data below is a random sample of 30 households regarding their monthly
electric bill. Determine the number of classes to use and make a frequency table and
histogram/polygon to represent the data.
31. 10.2 Measures of Central Tendency
• Ways to describe “on average…”
–Mean
• What is commonly thought of as
“average”
–Median
• The “middle” of the data
–Mode
• The data value that occurs most often
32. We need some data…
• Number of hits during spring training for 15
Phillies players: (alphabetical order)
21 19 10 1 6
28 32 11 2 15
2 17 21 29 21
33. Sample Mean
n
x
x
• The mean of a sample set of data
“x bar” is the
sample mean.
Round to
nearest
hundredth. (2
decimal places)
The sum of all
data values
The number of
data items
34. • Number of hits for 15 Phillies players:
21 19 10 1 6
28 32 11 2 15
2 17 21 29 21
67.15
15
211921
n
x
x
35. Median
• The “middle” of an ordered data set
– Arrange data in order
– Find middle value
• If n is odd, simply select middle value as the
median.
• If n is even, the median value will be the
mean of the two central values (since a
“middle” does not exist)
2
1
n
position
36. Finding Median Values
1. Median of the Phillies data.
2. Age (years) in the intensive care unit at
a local hospital.
68, 64, 3, 68, 70, 72, 72, 68
37. Median
• When is median a better indicator of “average”
than the mean?
38. Mode
• The data value that appears most often
– Single Mode
• One data value appears more than any other
– No Mode
• No data values repeat
– Multi-Mode
• There is a “tie” for the value that appears the most
