4. The file Exam_1, sheet named Top 50 Grad Programs includes data on the 50 top

Question

4. The file Exam_1, sheet named Top 50 Grad Programs includes data on the 50 top graduate programs in the United States, according to a 2009 U.S. News & World Report survey. a. Indicate the level of data measurements for Out-of-State tuition and fee levels. [Hint: Whether nominal, ordinal, interval or ratio.] b. Calculate the values of mean, median, and standard deviation (use =STDEV.P) for out-of-state tuition and fee levels. c. Calculate the skewness for out-of-state tuition and fee levels. Is the distribution of the out-of-state tuition and fee skewed? Negatively (left) or positively (right)? [Hint: think about the rule of thumb discussed in class i.e. if |SKEW| > 0.2, the data is skewed) d. Based on your answer for part (c), which measures, mean or median, should be used as a measure of central tendency? Why? e. Calculate the largest and smallest annual out-of-state tuition and fee levels. f. Find the annual out-of-state tuition and fee levels at each of the 25th, and 75th percentiles for these schools.

here is the data

School Overall Peers Recruiters GPA GMAT Accept Rate Salary Employed1 Employed2 Out of State Tuition and Fees Enrollment Harvard University (MA) 100 4.8 4.5 3.66 720 11.5% $144,261 87.0% 93.3% $50,830 1,801 Stanford University (CA) 99 4.8 4.5 3.64 726 7.5% $140,771 82.5% 92.6% $48,921 740 Northwestern University (Kellogg) (IL) 93 4.7 4.3 3.51 710 19.4% $130,365 89.3% 94.4% $46,791 1,254 University of Pennsylvania (Wharton) 93 4.8 4.3 3.50 714 16.3% $136,676 84.6% 89.1% $53,030 1,611 Massachusetts Institute of Technology (Sloan) 92 4.8 4.3 3.54 708 15.0% $131,087 79.0% 90.3% $47,034 788 University of Chicago 92 4.7 4.3 3.50 713 21.9% $130,839 87.4% 92.2% $47,938 1,144 University of California–Berkeley (Haas) 89 4.6 4.0 3.56 714 11.7% $126,886 85.1% 91.2% $40,605 500 Dartmouth College (Tuck) (NH) 87 4.3 4.1 3.44 712 16.0% $133,407 85.0% 93.6% $45,900 506 Columbia University (NY) 86 4.5 4.1 3.40 709 15.1% $130,281 78.2% 92.2% $48,566 1,234 Yale University (CT) 85 4.3 4.0 3.52 718 14.4% $117,366 75.6% 94.8% $47,300 382 New York University (Stern) 83 4.3 3.9 3.43 708 13.6% $128,968 82.0% 91.7% $43,942 841 Duke University (Fuqua) (NC) 82 4.4 4.0 3.40 696 30.4% $122,742 83.3% 91.7% $45,813 875 University of Michigan–Ann Arbor 81 4.4 4.0 3.32 706 20.1% $125,773 82.4% 85.3% $45,439 843 University of California–Los Angeles (Anderson) 80 4.2 3.9 3.50 711 19.5% $117,253 74.2% 88.9% $38,563 731 Carnegie Mellon University (PA) 79 4.0 3.8 3.35 690 28.3% $122,944 94.0% 96.2% $48,204 392 University of Virginia (Darden) 79 4.1 4.0 3.35 693 24.6% $126,362 85.1% 90.8% $45,500 644 Cornell University (Johnson) (NY) 78 4.2 3.9 3.30 697 20.6% $122,776 80.7% 90.7% $46,510 593 University of Texas–Austin (McCombs) 74 4.0 3.8 3.39 681 26.7% $116,484 82.4% 88.7% $40,900 540 Georgetown University (McDonough) (DC) 71 3.6 3.6 3.35 678 30.2% $114,463 87.9% 98.2% $41,934 522 University of North Carolina–Chapel Hill (Kenan-Flagler) 70 4.0 3.8 3.30 678 34.3% $110,202 78.5% 86.5% $42,239 562 University of Southern California (Marshall) 70 3.9 3.5 3.32 692 23.0% $104,382 80.1% 93.7% $44,502 426 Emory University (Goizueta) (GA) 69 3.8 3.7 3.40 680 28.1% $108,107 70.7% 86.0% $41,428 373 Georgia Institute of Technology (DuPree) 69 3.3 3.5 3.40 681 30.1% $105,266 92.7% 100.0% $32,076 154 Indiana University–Bloomington (Kelley) 69 3.8 3.7 3.35 663 34.0% $109,329 82.3% 89.7% $38,221 474 Washington University in St. Louis (Olin) 69 3.8 3.6 3.42 681 33.8% $103,184 76.6% 90.4% $41,586 294 Ohio State University (Fisher) 67 3.6 3.3 3.41 674 30.5% $101,146 80.8% 97.1% $37,845 277 University of Washington 67 3.4 3.6 3.38 688 30.9% $98,192 83.5% 96.2% $32,451 223 University of Wisconsin–Madison 65 3.6 3.3 3.36 666 33.1% $100,907 83.5% 94.2% $26,568 231 Arizona State University–Main Campus (W. P. Carey) 64 3.5 3.4 3.43 676 24.2% $94,599 72.9% 91.5% $29,856 170 Brigham Young University (Marriott) (UT) 64 3.1 3.5 3.52 673 56.4% $102,026 77.3% 94.5% $9,240 314 University of Rochester (Simon) (NY) 64 3.3 3.3 3.50 675 32.9% $97,206 79.3% 91.7% $40,005 352 Purdue University–West Lafayette (Krannert) (IN) 63 3.6 3.5 3.40 662 29.9% $96,470 78.4% 86.3% $34,940 293 Texas A&M University–College Station (Mays) 62 3.3 3.2 3.39 643 26.1% $96,485 91.2% 98.2% $28,022 164 University of Minnesota–Twin Cities (Carlson) 62 3.5 3.5 3.31 663 39.1% $104,745 78.6% 85.7% $39,238 199 University of Notre Dame (Mendoza) (IN) 62 3.4 3.4 3.30 677 34.1% $102,028 78.0% 90.7% $37,740 315 Vanderbilt University (Owen) (TN) 62 3.5 3.5 3.30 656 35.7% $103,262 75.5% 90.2% $40,917 390 University of Florida (Hough) 61 3.3 3.4 3.34 687 31.4% $84,990 82.3% 93.5% $24,066 142 Rice University (Jones) (TX) 60 3.3 3.2 3.29 667 31.1% $108,596 79.2% 89.6% $38,234 250 University of Illinois–Urbana-Champaign 60 3.5 3.3 3.40 639 34.9% $97,725 75.0% 88.8% $30,352 198 Michigan State University (Broad) 59 3.4 3.3 3.24 642 26.9% $104,445 81.7% 91.5% $29,183 214 Penn State University–University Park (Smeal) 59 3.4 3.4 3.20 646 27.8% $99,655 82.6% 92.8% $31,128 187 University of California–Davis 59 3.3 3.1 3.40 675 24.9% $93,712 76.3% 89.5% $36,894 120 University of Maryland–College Park (Smith) 59 3.5 3.1 3.34 660 27.8% $93,927 76.3% 89.2% $42,305 257 Boston College (Carroll) 58 3.4 3.2 3.30 661 27.9% $93,581 70.8% 90.8% $66,304 202 University of Iowa (Tippie) 58 3.2 3.1 3.37 653 38.7% $90,714 81.0% 95.2% $26,167 140 Boston University 57 3.1 3.1 3.38 680 27.8% $100,322 74.6% 83.3% $37,456 315 Southern Methodist University (Cox) TX 55 3.2 3.2 3.23 642 35.7% $94,361 76.8% 94.6% $39,308 171 Tulane University (Freeman) (LA) 54 3.1 2.9 3.30 655 59.7% $91,844 82.6% 93.5% $45,748 175 Babson College Olin) (MA) 53 3.4 3.3 3.18 630 47.8% $105,470 60.9% 84.8% $38,500 387 University of Texas–Dallas 53 2.8 3.2 3.70 651 32.7% $67,011 65.5% 89.7% $37,265 83

Explanation / Answer

a. The level of data measurements for Out-of-State Tuition and Fees is Ratio level.

b. mean = $ 39,870

median = $ 40,753

standard deviation = $ 8,908.418

c. The distribution skewness = -0.4945.

So the distribution is left skewed.

d. The median is usually preferred to other measures of central tendency when the data set is skewed.

e. The largest annual out-of-state tuition and fee level = $ 66,304

The smallest annual out-of-state tuition and fee level = $ 9,240

f. The percentile levels can be found using the Excel function PERCENTILE.INC()

The 25th percentile occurs at fee level: $ 36,986.75

The 25th percentile occurs at fee level: $ 45,796.75

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