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. For example: one gallon of regular gasoline cost $0.99 the in 1994 and $3.03 in So the gasoline price index number for 2007 with the year 1994 as the base period, is

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 price 0.50/pound 0.80/gallon 13.00/hour 1990 cost price 0.65/pound 1.50/gallon 22.00/hour 20.00/hour 1990 quantity 100 pounds 50 gallons 10 hours 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 = cost (using 1990 quantity)

How can We Use CPI 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 While the rate for today (2011) is 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, 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: Level of enrollment for undergraduate students – West Lafayette campus ( )

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

Bar Graphs: Level of enrollment for undergraduate students – West Lafayette campus ( )

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

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 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.

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

Line Graph: Striking Deviations 2 nd Industrial Revolution World War II

Line Graph: Seasonal Variation historical temperature at West Lafayette from Weather Underground

Line Graph: Seasonal Variation The period could be shorter!