1. The file Exam_1, sheet named Top 50 Grad Programs includes data on the 50 top
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Question
1. 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.
Out of State Tuition and Fees $50,830 $48,921 $46,791 $53,030 $47,034 $47,938 $40,605 $45,900 $48,566 $47,300 $43,942 $45,813 $45,439 $38,563 $48,204 $45,500 $46,510 $40,900 $41,934 $42,239 $44,502 $41,428 $32,076 $38,221 $41,586 $37,845 $32,451 $26,568 $29,856 $9,240 $40,005 $34,940 $28,022 $39,238 $37,740 $40,917 $24,066 $38,234 $30,352 $29,183 $31,128 $36,894 $42,305 $66,304 $26,167 $37,456 $39,308 $45,748 $38,500 $37,265Explanation / Answer
a. The out of state tution fees are quantitative data, which apart from classfication (high out of state tution fees, medium out of state tution fees and low out of state tution fees), can be ordered (less then average, average, above average) and the difference between the values consists of meaning. Therefore, out of state tution fees are measured in interval level of measurement.
b. Enter data in Excel-in the formula bar, type =Average(A1:A51), the average is 39870.08. Similarly, in the formula bar type, =Median(A1:A51), the median is 40752.5. In the formual bar, type, =STDEVP(A1:A51), the median is 8908.418.
c. Type =SKEW(A1:A51), the resultant value is -0.49453. According to rule, |skew|>0.2, therefore, the data is negatively skewed.
d. Since, the data is negatively skewed, median should be used as measure of central tendency as it is resistant to outliers.
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