Multiple choice

The mean of observations 2, x, 7, 3, y, 9, 6 is 6, where x and y are constants. If x is replaced by 3x + 1 and y is replaced by y + 3, then the mean increases by 2. Find the value of x.

  1. 7

  2. 5

  3. 10

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original mean is 6 for 7 observations, so sum = 42. This gives x + y = 15. After replacements, new sum = 56 (mean increases by 2 to 8). This gives 3x + y = 25. Subtracting the two equations: 2x = 10, so x = 5. You can verify by finding y = 10 and checking both conditions are satisfied.

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