Multiple choice

The numbers of books sold at a certain store over six of the last seven business days were 6, 8, 2, 9, 4, and 7, respectively. If the number of books sold on the seventh day was 3, 6, or 7, for which value is the average number of books sold per day equal to the median number of books sold per day?I. 3 II. 6 III. 7

  1. I only

  2. II only

  3. I and II only

  4. II and III only

  5. I, II, and III
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The six known values are 2, 4, 6, 7, 8, and 9, with a sum of 36. If the seventh value is 6, the sorted list is 2, 4, 6, 6, 7, 8, 9, which has a median of 6, and the average is (36 + 6) / 7 = 6. Testing 3 and 7 shows that their averages do not equal their respective medians.

AI explanation

We test the three possible values for the seventh day to see if the mean equals the median. If the seventh day is 6, the sum of all seven days is 42, making the mean 6; the sorted list is 2, 4, 6, 6, 7, 8, 9, and the median is also 6. Testing 3 gives a mean of about 5.57 and a median of 6, while testing 7 gives a mean of about 6.14 and a median of 7, so only the value 6 works.

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