Plan for Today:

Chapter 8: Measuring

Chapter 10: Graphs, Good and Bad

Chapter 16: The Consumer Price Index and Government Statistics

Measuring

Measuring:

There are two kinds of measurements: 1. Categorical measurements 2. Quantitative measurements

Measurements provide information about the individuals. They’re not always numbers.

e.g.: the weather and temperature for today

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.

valueindex number 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

3.03100 306

0.99

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.

Good or Service

Salt

Kerosene

Welding

Repairing

Total

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.

1990 price

0.50/pound

0.80/gallon

13.00/hour

1990 cost

50.00

40.00

130.00

2007 price

0.65/pound

1.50/gallon

22.00/hour

20.00/hour

1990 quantity

100 pounds

50 gallons

10 hours

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 isIndex number = 360 / 220 * 100 = 163.6

65.00

75.00

220.00

2007 cost(using 1990 quantity)

How can We Use CPI

dollars at time B CPI at time B

dollars at time A CPI at time A

We can use the formula to convert dollars of one year into dollars of another year and thus compare the buying power:

The CPI is a fixed market basket price index, with several hundred items that represent all consumer purchases.

Example:

The federal minimum wage rate for 1990 was 3.80. While the rate for today (2011) is 7.25. Is it enough?

7.25 CPI now 226.5

Dollars in 1990 CPI in 1990 130.7

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,

The result is 4.18.

Graphs, Good and Bad

Concepts:

A quantitative variable takes numerical values for which arithmetic operations such as adding and averaging make sense.

A categorical variable places an individual into one of several groups or categories.

To display the distribution of a categorical variable, use a pie chart or a bar graph

Pie Charts:

27%

22%21

%

29%

1%

FreshmenSophomoresJuniorsSeniorsNondegree

Level of enrollment for undergraduate students – West Lafayette campus (2011- 2012)

Pie Charts:

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

27%

22%21%

29%

1%

Bar Graphs:

Level of enrollment for undergraduate students – West Lafayette campus (2009- 2010)

0100020003000400050006000700080009000

10000

Number

Bar Graphs:

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

0100020003000400050006000700080009000

10000

Number

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

3030.230.430.630.8

3131.231.431.631.8

32

Number of undergraduate students enrolled at each year – West Lafayette campus (in thousands)

Line Graph

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.

3030.230.430.630.8

3131.231.431.631.8

32

Line Graph

Overall pattern (e.g., a trend is a long-term upward or downward movement over time.)

Striking deviations (or outliers)

When you deal with a line graph, pay attention to:

Seasonal variation

Line Graph

3030.230.430.630.8

3131.231.431.631.8

32

Number of undergraduate students enrolled at each year – West Lafayette campus (in thousands)

Line Graph: Striking Deviations

2nd Industrial Revolution

World War II

Line Graph: Seasonal Variation

historical temperature at West Lafayette fromWeather Underground

0

10

20

30

40

50

60

70

80

90

Jan-

08

Apr-

08

Jul-0

8

Oct

-08

Jan-

09

Apr-

09

Jul-0

9

Oct

-09

Jan-

10

Apr-

10

Jul-1

0

Oct

-10

Jan-

11

Apr-

11

Jul-1

1

Oct

-11

Jan-

12

Line Graph: Seasonal Variation

The period could be shorter!