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One-variable data: Distributions and measures of center and spread SAT question

Math · Problem-Solving and Data Analysis · Easy · Answer it here, explanation included.

Number of High School Students Who
Completed Summer Internships
High schoolYear
20082009201020112012
Foothill8780757670
Valley4454657682
Total131134140152152

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?

  1. The mean number from Foothill High School is greater than the mean number from Valley High School.
  2. The median number from Foothill High School is greater than the median number from Valley High School.

ExplanationShow

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 the fraction with numerator 87 plus 80, plus 75, plus 76, plus 70, and denominator 5, equals, the fraction 388 over 5, or 77.6. Similarly, the mean number from Valley High School is the fraction with numerator 44 plus 54, plus 65, plus 76, plus 82, and denominator 5, equals, the fraction 321 over 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.

Choices A, B, and D are incorrect and may result from various misconceptions or miscalculations.

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