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are106-homework-2-key - ARE106 Homework#2AK ARE106 Homework...

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ARE106 Homework #2 AK ARE106 – Homework 2 Answer Key 1. Questions related to data file data2-2. (i)Click on ‘Data’, then click on ‘Read info’ to see the following: DATA2-2: High school and College GPA of undergraduate students Data reflect the first year achievement. colgpa = Grade point average in college (Range 0.85 - 3.97) hsgpa = High school GPA (Range 2.29 - 4.5) (ii)This is a cross-section dataset as the data are for a specific point in time. We do not have measurements of the same variable for different points in time here; we only have one data point for high school GPA and one data point for college GPA. (iii) Within range – there are some values of the college GPA that are well below 2. The lowest value of colgpa is 0.85 for observation 416. There are also some unusual values of hsgpa, such as values that exceed 4. The highest hsgpa is 4.5 for observation 411. Obvious errors – it is possible that values for hsgpa exceeding 4.0 are errors; however, many high schools allow for grade point averages exceeding 4.0 if students take Advanced Placement (AP) classes. Therefore, there are no “obvious” errors in the dataset. Surprises – There are some surprising observations; specifically, those where the difference between colgpa and hsgpa is unusually large. The observations where the difference exceeds 2 are the following: Obs colgpa hsgpa diff 390 1.57 3.6 2.03 380 1.57 3.67 2.1 61 1.11 3.21 2.1 92 1.84 4 2.16 416 0.85 3.04 2.19 386 1.81 4.07 2.26 Overall impression – In general, hsgpa is greater than colgpa, which is what we would expect before seeing the data as grades generally decline in college. 1
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ARE106 Homework #2 AK (iv) The summary statistics are below. The means are highlighted and support the conclusion reached in (iii) as the mean of hsgpa (3.5578) is greater than the mean of colgpa (2.7855). The variance of hsgpa is 0.17605 (=0.41958 2 ). The coefficient of variation (aka CV) for hsgpa is 0.11793. The coefficient of variation uses the standard deviation rather than the variance because the units of variance are squared (e.g., gpa squared) while the units of the standard deviation are identical to those of the variable of interest. In calculating CV, using the standard deviation instead of the variance allows us to divide out the units resulting in a unit-less measurement of the spread. The CV is defined as “ a measure of the dispersion of a distribution relative to its mean ” (Ramanathan, pg. 26). We might use CV when we are interested in a measure of spread
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are106-homework-2-key - ARE106 Homework#2AK ARE106 Homework...

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