Transcript Slide 1

Plan for Today:
Chapter 8: Measuring
Chapter 16: The Consumer Price Index and Government
Statistics
Chapter 10: Graphs, Good and Bad
Measuring
Measuring:
Measurements provide information about the individuals.
They’re not always numbers.
e.g.: the weather and temperature for today
There are two kinds of measurements:
1. Categorical measurements
2. Quantitative measurements
How to tell the difference: Can they be added up?
Three Properties of Measurements:
Valid: if it is relevant
Bias: systematically favors certain outcomes
Reliable: if the random error is small
Three Properties of Measurements:
The Consumer Price Index and
Government Statistics
Why CPI?
What to compare the buying power (e.g. salary and
living cost) between years.
Dollar itself is not a good index. e.g.: inflation
Before we introduce CPI, we need to introduce two
more terms: index number and Fixed market basket
price index.
Index Numbers:
The CPI is a new kind of numerical description, an index
number.
An index number measures the value of a variable
relative to its value at a base period.
index num ber 
value
 100
base value
For example: one gallon of regular gasoline cost $0.99 the in 1994
and $3.03 in 2007. So the gasoline price index number for 2007
with the year 1994 as the base period, is
3.03
0.99
 100  306
Fixed market basket price indexes:
A fixed market basket price index is an index number for
the total cost of a fixed collection of goods and services.
It computes the cost of the same collection of goods and
services over time.
The Mountain Man Price Index (Page 341):
Bill Smith lives in a cabin in the mountains and strives for
self-sufficiency . In 1990, he buys only salt, kerosene and
the service of a professional welder. In 2007, he also hired
someone to repair his cabin.
Good or
Service
1990 quantity
1990 price
1990 cost
2007 price
2007 cost
(using 1990 quantity)
Salt
100 pounds
0.50/pound
50.00
0.65/pound
65.00
Kerosene
50 gallons
0.80/gallon
40.00
1.50/gallon
75.00
Welding
10 hours
13.00/hour
130.00
22.00/hour
220.00
Repairing
Total
20.00/hour
220.00
360.00
We use 2007 prices to calculate the 2007 cost of this same
collection of goods and services. (Ignore any changes.)
The Mountain Man Price Index (set 1990 =100) for 2007 is
Index number = 360 / 220 * 100 = 163.6
How can We Use CPI
The CPI is a fixed market basket price index, with
several hundred items that represent all consumer
purchases.
We can use the formula to convert dollars of one year
into dollars of another year and thus compare the buying
power:
dollars at tim e B
dollars at tim e A

C P I at tim e B
C P I at tim e A
Example:
The federal minimum wage rate for 1990 was 3.80.
While the rate for today (2011) is 7.25. Is it enough?
In order to compare the buying power, we can transfer
the rates for 2011 and 1990 into the dollars in a same
year, for example,
7.25
D ollars in 1990
The result is 4.18.

C P I now
C P I in 1990

226.5
130.7
Graphs, Good and Bad
Concepts:
A categorical variable places an individual into one of several
groups or categories.
A quantitative variable takes numerical values for which
arithmetic operations such as adding and averaging make
sense.
To display the distribution of a categorical variable, use a pie
chart or a bar graph
Pie Charts:
1%
29%
27%
Freshmen
Sophomores
Juniors
Seniors
Nondegree
21%
22%
Level of enrollment for undergraduate students – West
Lafayette campus (2011- 2012)
Pie Charts:
1%
29%
21%
27%
22%
Pie charts show how a whole is divided into parts.
- the circle represents the whole (e.g. 30,836 undergrad students)
- the angle spanned by each wedge in proportion to the size of
that part
Bar Graphs:
Number
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
Level of enrollment for undergraduate students – West
Lafayette campus (2009- 2010)
Number
Bar Graphs:
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
Bar graphs show the value for each individual category.
- The height of each bin represents the value for that category.
- Bar graphs can compare quantities that are not parts of a whole
Line Graph
Many quantitative variables are measured at intervals
over time. Our main interest is change over time.
To display change over time, make a line graph.
Line Graph
32
31.8
31.6
31.4
31.2
31
30.8
30.6
30.4
30.2
30
Number of undergraduate students enrolled at each
year – West Lafayette campus (in thousands)
Line Graph
32
31.8
31.6
31.4
31.2
31
30.8
30.6
30.4
30.2
30
Always put time on the horizontal scale of your plot and
the variable you are measuring on the vertical scale.
Connect the data points by lines to display the change
over time.
Line Graph
When you deal with a line graph, pay attention to:
Overall pattern (e.g., a trend is a long-term upward or
downward movement over time.)
Striking deviations (or outliers)
Seasonal variation
Line Graph
32
31.8
31.6
31.4
31.2
31
30.8
30.6
30.4
30.2
30
Number of undergraduate students enrolled at each
year – West Lafayette campus (in thousands)
Line Graph: Striking Deviations
World War II
2nd Industrial Revolution
Line Graph: Seasonal Variation
90
80
70
60
50
40
30
20
10
historical temperature at West Lafayette from
Weather Underground
Jan-12
Oct-11
Jul-11
Apr-11
Jan-11
Oct-10
Jul-10
Apr-10
Jan-10
Oct-09
Jul-09
Apr-09
Jan-09
Oct-08
Jul-08
Apr-08
Jan-08
0
Line Graph: Seasonal Variation
The period could be shorter!