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Statistics: AP of Mean, Median, Mode

XAT 2011 · Quantitative Ability & Data Interpretation · Hard · Statistics

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In a list of 7 integers, one integer, denoted as x is unknown. The other six integers are 20, 4, 10, 4, 8, and 4. If the mean, median, and mode of these seven integers are arranged in increasing order, they form an arithmetic progression. The sum of all possible values of x is

  1. A.

    26

  2. B.

    32

  3. C.

    34

  4. D.

    38

  5. E.

    40

Answer

E

Explanation

Known integers: 4,4,4,8,10,204, 4, 4, 8, 10, 20. Mode = 4. Mean =50+x7= \frac{50 + x}{7}. Case 1: x=6  ⟹  x = 6 \implies Median = 6, Mean = 8. AP: 4, 6, 8. Case 2: x=34  ⟹  x = 34 \implies Median = 8, Mean = 12. AP: 4, 8, 12. Sum of possible xx values =6+34=40= 6 + 34 = 40.

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