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Mathematics: Standard Multiple Choice

Read the following SAT test question and then select your answer. 
ROC_QOTD_Jan_2011_1_fig_1.gif
The graph above shows the distribution of the number of days spent on business trips in 2010 by a group of employees of Company W. Based on the graph, what is the median number of days spent on business trips in 2010 for these employees?
The first thing you should do with any math question is read carefully. Always look closely at graphs; it is easy to make careless mistakes by misreading the labels or other information on a graph. This bar graph shows the number of employees who spent 20 or more days on business trips, separated by the number of days they spent traveling. Also look for key words in the question text; this one asks about the median number of days. Immediately ask yourself, "What is a median?" If you don't remember, make time to study math terminology between now and the SAT so that these words don't cost you time. The median of any set is the middle number when all members of the set are listed in order. This is not the same as an average (mean). The median of a set {1, 2, 3, 4, 5} is 3, and the median of a set {1, 2, 3, 4, 500} is also 3

After reading carefully, identify the Bottom Line. The last thing this problem asks is, "what is the median number of days spent on business trips in 2010 for these employees?" Put this in shorthand at the top of your scratch work. 




median=?    or    m=?

How do you find the median? This is when you ask, "What could I do?" You have two options here: Write out "20, 20, 20, 20, 20, 21, 21, 21..." and then count to the middle, or determine the middle and then find its place on the graph. On the SAT, the long way is the wrong way, so use the second method. 

First, calculate the total number of employees. 5+6+5+8+6+1=31 employees. Divide this by two to find the middle employee. Note that this method is different from the average formula, which would have required you to add up the total number of days all employees spent on business trips. If you lined these employees up along a hallway and then walked half the hallway, you would stop at the 15.5 mark, or the 16th employee. The 16th employee marks your median because there are 15 employees before her and 15 employees after her. 

Finally, look at the graph to determine how many days the 16th employee spent traveling for work. The first column accounts for five employees, and the second column brings the total up to 11. The third column includes employees 12-16, inclusive, and each of these employees spent 22 days on business trips. 

The answer is A, 22 days. 

The College Board reports that 32% of those who attempted this question got it right.



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