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!