Maths-
SAT
Easy

Question

In spring 2015, three separate studies on the fitness level of tenth graders were  conducted in the city of Mistwick. In each study, every student in a group of tenth  graders took the same fitness test and received a score on it. The possible scores on  the fitness test are the whole numbers from 50 to 100, inclusive. The distribution of the scores for each of the' studies is shown in the table below.

Score range

Study I

Study II

Study III

50-59

24

50

88

60-69

36

67

67

70-79

22

52

65

80-89

11

14

41

90-100

7

17

39

Mean score

68.6

68.7

70.4

Total number of participants

100

200

300

The participants for the studies were selected as follows.
• For Study I, 100 tenth graders were selected at random from all tenth graders in Mistwick.
• For Study II, 200 tenth graders were selected at random from all tenth graders in Mistwick.
• For Study III, 300 tenth graders from Mistwick volunteered to participate.
No tenth grader participated in more than one of the three studies.
Which of the following could be the median score in Study III?

  1. 59
  2. 68
  3. 70
  4. 82

The correct answer is: 68


    The total students in study – III are 300.
    Half of them = 150
    The cumulative frequency containing 150 is in 60 – 69 range
    So, the median is L plus fraction numerator N over 2 minus F over denominator f end fraction cross times h
    equals 60 plus fraction numerator 150 minus 88 over denominator 67 end fraction cross times 9
    =68.32 = 68

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