What is the result when the mean number of pets is subtracted from the median number of pets?

Question

The table shows the distribution of the number of pets owned by each of the 40 students in a class. Two of the frequencies, a and b, are not shown.

Number of pets: 0 | 1 | 2 | 3 | 4
Number of students: 9 | a | b | 6 | 3

The mean number of pets owned by the 40 students is 1.75.

Accepted Answer

0.25 or .25 or 1/4. Since there are 40 students, 9 + a + b + 6 + 3 = 40, so a + b = 22. The total number of pets is 40(1.75) = 70, so 0(9) + 1(a) + 2(b) + 3(6) + 4(3) = 70, giving a + 2b + 30 = 70, or a + 2b = 40. Subtracting the first equation gives b = 18 and a = 4. Listing the 40 values in order, positions 1–9 are 0s, positions 10–13 are 1s, and positions 14–31 are 2s; the 20th and 21st values are both 2, so the median is 2. Therefore 2 − 1.75 = 0.25. Common wrong answers: −0.25, from reversing the order of subtraction; 0.5, from taking the median as the middle of the list of *values* 0, 1, 2, 3, 4 while forgetting the missing frequencies must first be found; and 1.5, from averaging the 1 and 2 categories because the 20th and 21st entries were assumed to fall in different categories.

Problem-Solving and Data Analysis practice question

Answer: 0.25 or .25 or 1/4

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