SECTION 1.2 Data Classification 11 The two highest levels of measurement consist of quantitative data only. Data at the interval level of measurement can be ordered, and meaningful differences between data entries can be calculated. At the interval level, a zero entry simply represents a position on a scale; the entry is not an inherent zero. Data at the ratio level of measurement are similar to data at the interval level, with the added property that a zero entry is an inherent zero. A ratio of two data entries can be formed so that one data entry can be meaningfully expressed as a multiple of another. DEFINITION An inherent zero is a zero that implies “none.” For instance, the amount of money you have in a savings account could be zero dollars. In this case, the zero represents no money; it is an inherent zero. In contrast, a temperature of 0°C does not represent a condition in which no heat is present. The 0°C temperature is simply a position on the Celsius scale; it is not an inherent zero. To distinguish between data at the interval level and at the ratio level, determine whether the expression “twice as much” has any meaning in the context of the data. For instance, $2 is twice as much as $1, so these data are at the ratio level. In contrast, 2°C is not twice as warm as 1°C, so these data are at the interval level. Classifying Data by Level Two data sets are shown at the left. Which data set consists of data at the interval level? Which data set consists of data at the ratio level? Explain your reasoning. (Source: Major League Baseball) SOLUTION Both of these data sets contain quantitative data. Consider the dates of the Yankees’ World Series victories. It makes sense to find differences between specific dates. For instance, the time between the Yankees’ first and last World Series victories is 2009 - 1923 = 86 years. But it does not make sense to say that one year is a multiple of another. So, these data are at the interval level. However, using the home run totals, you can find differences and write ratios. For instance, Boston hit 22 more home runs than Cleveland hit because 81 - 59 = 22 home runs. Also, Chicago hit about 1.25 times as many home runs as Baltimore hit because 96 77 ≈ 1.25. So, these data are at the ratio level. TRY IT YOURSELF 3 For each data set, determine whether the data are at the interval level or at the ratio level. Explain your reasoning. 1. The body temperatures (in degrees Fahrenheit) of an athlete during an exercise session 2. The heart rates (in beats per minute) of an athlete during an exercise session Answer: Page A35 New York Yankees’ World Series victories (years) 1923, 1927, 1928, 1932, 1936, 1937, 1938, 1939, 1941, 1943, 1947, 1949, 1950, 1951, 1952, 1953, 1956, 1958, 1961, 1962, 1977, 1978, 1996, 1998, 1999, 2000, 2009 2020 American League home run totals (by team) Baltimore 77 Boston 81 Chicago 96 Cleveland 59 Detroit 62 Houston 69 Kansas City 68 Los Angeles 85 Minnesota 91 New York 94 Oakland 71 Seattle 60 Tampa Bay 80 Texas 62 Toronto 88 EXAMPLE 3 For help with basic mathematical symbols and Greek letters and addition and subtraction of integers, see Integrated Review at MyLab Statistics
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