Variable: Size
Decimal point is 1 digit(s) to the left of the colon.
1:2
1 : 5555556666666777777778888889
2 : 01333
2 : 5555566789
3 : 223
3:5
= 0.12
1,7,14,22,28,29,30,31,34,39,41,42,43,44,46,47,48
This is the number of observations being summed up by co
Examples:
Raw scores on behavioral tests are often transformed for easier comparison. A test of reading
ability has mean 57 and standard deviation 10 when given to third graders. Sixth graders have
mean score 83 and standard deviation 5 on the same test.
zscores = a measure of relative standing? Well, relative frequencies are
just proportions, so zscores must also be divided by something.
If you need to compare unlike sets of observations, i.e., datasets with
different means and sds, you can use zscore
You should always plot your data
first!
But which plot should you use?
The individual histograms however show the
differences in the three variables.
The moral of the story is that summary numbers and
graphs (i.e., boxplots) lose some sometimes valuable
i
GRAPHS
PROBLEMS WELL STUDY
1. Often, the bottom or leftmost point on an axis should be 0. If the axis shows the year, this isnt true.
2. We want to compare apples to apples. Control for inflation, population growth. When youre plotting
multiple things on
Response Variable (Dependent) The outcome variable on which comparisons are made
Explanatory variable (Independent)
o
o
Categorical: defines the groups to be compared with respect to value on the response variable
Quantitative: defines the change in diff
Changing units of
measurement: shift and scale
Variables can be recorded in different units of measurement. Most
changes
often, one measurement unit is a linear transformation of another
measurement unit: xnew = a + b*x, where a is a shift change and b is
An ecologist was interested in how the distribution of ﬁsh in a lake was changing over time.
The current study of 1028 ﬁsh contained 523 catﬁsh. The ecologist estimated that 50.9% of
the ﬁsh in the lake were catﬁsh.
Which of the following is (are) the var
Distributions
%
xx
%
xx
%
xx
%
xx
%
xx
%
xx
%
xx
%
xx
No r m a l
Un i fo r m
S k Ri gh t
S k L e ft
25
%
20%
15
%
10%
5
%
25
%
20%
15
%
10%
5
%
0.00
10.00
20.00
30.00
0.00
da t a
DATA StemandLeaf Plot for
TYPE= Normal
Frequency
Stem &
1.00 Extremes
1.00
Graphs and Statistics for Categorical (Qualitative Data)
Graphs
Pie chart
Bar
chart(graph)
Pros
Cons
very easy to read, highly visible
data needs to sum to 100% and best for only a few
categories
any number of cats and different pops, easier to
compare
th
Lab 03a
I. Is yawning contagious?1
On the TV show Mythbusters, they investigated whether yawning is contagious. (Link on Blackboard.)
The data from the final study at the local flea market is included below. People chosen for the study were randomly assig
Probabilities of a TwoWay Table
Grades
Males
Females
Totals
A
r1c1
r1c2
R1
B
r2c1
r2c2
R2
C
r3c1
r3c2
R3
row total
D
r4c1
r4c2
R4
column total
C1
C2
Grand Total
Totals
cell
count
Sum of all
the data
Joint Probabilities: the cell counts divided by the gra
~
Q1 x
min
Q3
max
1,2,5,5,7,8,10,11,12,12,18,25
1
5
9
12
18
5.5
25
22.5
1.5IQR
5  1.5 * 7 = 5.5
IQR = 12 5 = 7
1.5IQR
12 + 1.5 * 7 = 22.5
25 is considered an outlier and will be a point in a boxplot and the
whisker ends at the last nonoutlier data poi
Section 1.1
Data:
open to interpretation
needs to be understood to be appreciated
Types of Data
categorical or qualitative
numeric or quantitative
Descriptive Statistics of Categorical Data
Summary numbers
o
Counts
o
Proportions
o
Locations
(sometimes

x