MM207 Statistics Welcome to the Unit 2 Seminar name

Accessing StatCrunch

Data Types Quantitative data Quantitative data has a value or a numerical measurement for which you can calculate sums, products and other numerical calculations. You can do meaningful math Qualitative data Qualitative data is grouped into a category or group. Sums, products or other numerical calculations do not mean anything. You cannot do meaningful math

Quantitative Data Continuous data can take on any value in a given interval Age: between 10 years and 11 years old there can be any number between, 10.4, 10.45, , , 10.89, Discrete data can take on only particular, distinct values and not other values in between Number of children in a family must be and will only be a whole number

Levels of Measurement Nominal: Data is put in categories [names] Ordinal: Nominal plus the data is put in ordered categories [ranks] Interval: Ordinal plus the interval is meaningful, but ratios are not [arbitrary zero] Ratio: Interval plus the data have an absolute (meaningful) zero point [ratios are meaningful]

Types of Error Random errors occur because of random and inherently unpredictable events in the measurement process Systematic errors occur when there is a problem in the measurement system that affects all measurements in the same way

Size of the Error Absolute error describes how far a claimed or measured value is from the true value Relative error compares the size of the absolute error to the true value [percentage]

Size of the error Find the absolute and relative error. Your true weight is 100 pounds, but a scale says you weigh 105 pounds. Solution: The measured value is the scale reading of 105 pounds and the true value is 100 pounds. absolute error = measured value – true value = 105 lbs – 100 lbs = 5 lbs relative error = absolute error / true value x 100% 5 lbs/100 lbs. x 100% = 5%

Describing Results Accuracy describes how closely a measurement approximates a true value. An accurate measurement is close to the true value. (Close is generally defined as a small relative error, rather than a small absolute error.) Precision describes the amount of detail in a measurement.

Describing Results Suppose that your true weight is pounds. The scale at the doctor’s office, which can be read only to the nearest quarter pound, says that you weigh 102¼ pounds. The scale at the gym, which gives a digital readout to the nearest 0.1 pound, says that you weigh pounds. Which scale is more precise? Which is more accurate?

The absolute change describes the actual increase or decrease from a reference value to a new value: absolute change = new value – reference value The relative change describes the size of the absolute change in comparison to the reference value and can be expressed as a percentage: relative change = new value – reference value x 100% reference value

Absolute/Relative Change World population in 1950 was 2.6 billion. By the beginning of 2000, it had reached 6.0 billion. Describe the absolute and relative change in world population from 1950 to Absolute Change: 6.0 – 2.6 = 3.4 billion Relative Change: ( )/2.6 * 100 = 130%

Absolute and Relative Differences The absolute difference is the difference between the compared value and the reference value: absolute difference = compared value - reference value The relative difference describes the size of the absolute difference in comparison to the reference value and can be expressed as a percentage: relative difference = (compared value – reference value) x 100% reference value

Absolute and Relative Differences Life expectancy for American men is about 75 years, while life expectancy for Russian men is about 59 years. Compare the life expectancy of American men to that of Russian men in absolute and relative terms. Solution: Absolute Difference: 75 – 59 = 16 years Relative Difference: (75-59)/ 59 * 100 = 27%

Percentages of Percentages Percentage Points versus % When you see a change or difference expressed in percentage points, you can assume it is an absolute change or difference. If it is expressed as a percentage, it probably is a relative change or difference.

Percentages of Percentages Based on interviews with a sample of students at your school, you conclude that the percentage of all students who are vegetarians is probably between 20% and 30%. Should you report your result as “25% with a margin of error of 5%” or as “25% with a margin of error of 5 percentage points”? Explain.

Index Numbers

Index Numbers Suppose the cost of gasoline today is $3.20 per gallon. Using the 1975 price ($0.567) as the reference value, find the price index number for gasoline today. Table 2.1 shows that the price of gas was 56.7¢, or $0.567, per gallon in If we use the 1975 price as the reference value and the price today is $3.20, the index number for gasoline today is index number = $3.20/$0.67 x 100 = This index number for the current price is 564.4, which means the current gasoline price is 564.4% of the 1975 price.

Consumer Price Index The Consumer Price Index (CPI), which is computed and reported monthly, is based on prices in a sample of more than 60,000 goods, services, and housing costs.

Consumer Price Index Suppose you needed $30,000 to maintain a particular standard of living in How much would you have needed in 2006 to maintain the same living standard?

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