Chapter 21: Identify The Following Variables As Either Quali

Chapter 21 Identify The Following Variables As Either Qualitative Or

Identify the following variables as either qualitative or quantitative, and explain your answers. Additionally, determine whether the number is continuous or discrete, identify the most appropriate level of measurement for each case, and perform relevant calculations where required.

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The first task involves distinguishing between qualitative and quantitative variables. A qualitative variable describes qualities or categories, typically non-numeric in nature, whereas a quantitative variable measures numerical quantities and can be subjected to arithmetic operations. For example, the number of people on a jury is a quantitative variable because it is a countable number, reflecting an attribute that can be measured. On the other hand, the color of a house is qualitative because it describes a category without inherent numerical value.

Within quantitative variables, it is important to specify whether they are continuous or discrete. Continuous variables can take any value within a range and are often measured, such as height; discrete variables are countable and take on a finite or countably infinite set of values, like the number of limbs. The average height of all freshmen entering college, which is 68.4 inches, is continuous because height can vary continuously and can theoretically take any value within a range. Conversely, the number of limbs on a 2-year-old oak tree, which is 21, is discrete because it is a countable number of limbs.

The levels of measurement are essential to classify variables properly as they determine the types of statistical analyses appropriate. The four levels are nominal, ordinal, interval, and ratio. The temperature in degrees Fahrenheit of ocean depths is most suitably measured at the interval level because the differences are meaningful, but there is no true zero point. The rank of individuals in the military is an ordinal variable because it reflects a hierarchy without quantifying the exact difference between ranks. The number of people with different hair colors in a classroom is a ratio level variable, as it involves counts with a natural zero point.

Further, specific calculations involve understanding errors, unit conversions, and percentage differences. The absolute error of the microprocessor speed measurement is the absolute difference between the measured value and the true value: 820 MHz - 800 MHz = 20 MHz. The relative error is the absolute error divided by the true value, expressed as a percentage: (20 / 800) * 100% = 2.5%. Converting fractions and decimals to percentages involves multiplying by 100; thus, 1/16 = 6.25%. Similarly, 0.45 is equivalent to 45%.

The percentage difference between two averages, such as $115 for humanities majors and $70 for mathematics majors, is calculated relative to the average for mathematics majors: ((115 - 70) / 70) 100% ≈ 64%. The Statistics Text Index measures the price change over time relative to an initial price. Calculated as ((price in 2000 / price in 1985) - 1) 100, the index is ((100 / 50) - 1) 100 = 1 100 = 100%, indicating the price doubled over the period.

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