SECTION 2.5 Measures of Position 103 Using Technology to Find Quartiles The costs of tuition and fees (in thousands of dollars) for 25 liberal arts colleges are listed. Use technology to find the first, second, and third quartiles. What do you observe? (Source: U.S. News & World Report) 55 59 55 56 57 55 60 59 61 58 57 61 59 48 44 30 39 58 48 46 19 55 45 48 48 SOLUTION Minitab and the TI-84 Plus, for instance, each have features that calculate quartiles. Use such technology to find the first, second, and third quartiles of the tuition data. From the displays, you can see that Q1 = 47, Q2 = 55, and Q3 = 58.5. TI-84 PLUS 1-Var Stats Çn=25 minX=19 Q1=47 Med=55 Q3=58.5 maxX=61 MINITAB Descriptive Statistics: Tuition Variable N Mean SE Mean StDev Minimum Tuition 25 51.20 2.04 10.18 19.00 Variable Q1 Median Q3 Maximum Tuition 47.00 55.00 58.50 61.00 STATCRUNCH Summary statistics: Column Q1 Median Q3 Tuition 48 55 58 Interpretation About one quarter of these colleges charge tuition of $47,000 or less; about one half charge $55,000 or less; and about three quarters charge $58,500 or less. TRY IT YOURSELF 2 The costs of tuition and fees (in thousands of dollars) for 25 universities are listed. Use technology to find the first, second, and third quartiles. What do you observe? (Source: U.S. News & World Report) 58 35 49 11 31 56 25 18 36 31 10 32 35 19 39 49 33 27 55 33 55 46 28 54 57 Answer: Page A37 The median (the second quartile) is a measure of central tendency based on position. A measure of variation that is based on position is the interquartile range. The interquartile range tells you the spread of the middle half of the data, as shown in the next definition. EXAMPLE 2 Tech Tip Note that you may get results that differ slightly when comparing results obtained by different technology tools. For instance, in Example 2, the first quartile, as determined by Minitab, the TI-84 Plus, and the Quartile.exc function of Excel, is 47, whereas the result using StatCrunch and the Quartile.inc function of Excel is 48. EXCEL A B 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2 55 56 57 55 60 59 61 47 55 58.5 58 57 61 59 48 44 30 39 58 48 46 21 22 23 24 25 19 55 45 48 48 55 59 =Quartile.exc(A1:A25,2) =Quartile.exc(A1:A25,3) =Quartile.exc(A1:A25,1) 48 55 58 =Quartile.inc(A1:A25,2) =Quartile.inc(A1:A25,3) =Quartile.inc(A1:A25,1)
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