# QMB6357 Unit 2 HW

**Topics:**Arithmetic mean, Standard deviation, Median

**Pages:**5 (797 words)

**Published:**October 29, 2014

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Fifty undergraduate students answered a survey. The results are shown here.

Q-2a: What is the average expected salary of these undergraduates upon graduation? (Round to two decimals)

Q-2b: What is the median amount spent on textbooks? (Round to two decimals)

Q-2c: What is the mode with respect to the number of affiliations to clubs and other organizations of these undergraduates?

Q-2d: What is the standard deviation of these students' GPAs? (Round to two decimals)

Q-2e: Using coefficients of variation, tell me which has more variation, the age of the students in this sample or the amounts that they spent on textbooks.

ANSWERS

Q-2a) The average expected salary, or the mean salary, of undergraduates upon graduation can be found by using the function =AVERAGE(range of salaries)

47.3

The formula is the equivalent of adding all of the salaries and dividing it by the total number of students surveyed.

The average expected salary of undergraduates upon graduation is 47.3, or, if salary is expressed in thousands, then the average expected salary of undergraduates is $47,300.

Q-2b) The median amount spent on textbooks, or, the middle number when all amounts are listed in numerical order, can be found by using the function =MEDIAN(range of numbers)

450

The median amount students spent on textbooks is $450. That is, if all of the amounts were listed in numerical order, the number in the middle would be $450. Or, if there are an even number of data, such as in this example, then the median number is the average of the middle 2 numbers.

Q-2c) The mode, or the number that appears the most amount of times in the given data, can be found with the function =MODE(range of numbers).

0

The mode with respect to the number of affliciations to club and other organizations is 0; that is that most students have NO affliations to clubs and other organizations.

Q-2d) The standard deviation of the students' GPAs measures how spread out the numbers are from the mean, or average, of the data. To find the standard deviation, we can use the formula =STDEV(range of numbers)

0.399650664

The standard deviation of the students' GPA (rounded to two decimals) is .40. This tells us that the data varies from the mean .40 GPA points.

Q-2e) The coefficients of variation is a way to compare the relative variability of 2 data sets. It essentially is a ratio of the standard deviation to the mean.The first step in comparing the variation between the age of students and the amounts they spend on books, we must first find the standard deviation of each. This can be done using the formula =STDEV(range of numbers)

3.343955863Standard Deviation for Age of Students

135.9809786Standard Deviation for Amount Spent on Textbooks

Next we must find the average, or mean, of each of the data sets by using the formula =AVERAGE(range of numbers)

20.96Average Age of Students

470.7Average Amount Spent on Textbooks

Then, to find their coefficient of variation, we must divide their standard deviations by their averages, or

3.35/20.96 = 0.16 Coefficient of Variation for Age of Students135.98/470.7 = 0.29 Coefficient of Variation for Amount Spent on Textbooks

The larger the coefficient of...

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