SAT question 6670e407 (Distributions, Center & Spread)

Question

The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools. Which of the following statements are true about the number of students who completed summer internships for the $5$ years shown?

I. The mean number from Foothill High School is greater than the mean number from Valley High School.

II. The median number from Foothill High School is greater than the median number from Valley High School.

College Board · Accepted Answer

The correct answer is C. Choice C is correct. The mean of a data set is found by dividing the sum of the values by the number of values. Therefore, the mean number of students who completed summer internships from Foothill High School is (87 + 80 + 75 + 76 + 70)/5 = (388)/5 , or 77.6 . Similarly, the mean number from Valley High School is (44 + 54 + 65 + 76 + 82)/5 = (321)/5 , or 64.2 . Thus, the mean number from Foothill High School is greater than the mean number from Valley High School. When a data set has an odd number of elements, the median can be found by ordering the values from least to greatest and determining the value in the middle. Since there are five values in each data set, the third value in each ordered list is the median. Therefore, the median number from Foothill High School is 76 and the median number from Valley High School is 65 . Thus, the median number from Foothill High School is greater than the median number from Valley High School.

Number of High School Students Who Completed Summer Internships
High school	Year
	$2008$	$2009$	$2010$	$2011$	$2012$
Foothill	$87$	$80$	$75$	$76$	$70$
Valley	$44$	$54$	$65$	$76$	$82$
Total	$131$	$134$	$140$	$152$	$152$

Explanation

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Why the other choices are wrong

SAT Question 6670e407: Distributions, Center & Spread answer and explanation with Desmos solution

Explanation

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Why the other choices are wrong