Multiple choice

In a data set, the frequency of occurrence of 4, 6, 8, 2, 5 is y, y - 3, y - 8, y - 2, y + 5. If the mean of the data set is 25, what is the value of y? (up to one decimal place)

  1. 1.2

  2. 1.4

  3. 1.8

  4. 2.2
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B Correct answer
AI explanation

Using the direct method for the arithmetic mean, we set the sum of (value * frequency) divided by the sum of frequencies equal to 25. This gives the equation (4y + 6(y-3) + 8(y-8) + 2(y-2) + 5(y+5)) / (y + y-3 + y-8 + y-2 + y+5) = 25. Simplifying the numerator yields 26y - 55 and the denominator yields 5y - 8, leading to 26y - 55 = 25(5y - 8). Solving 99y = 145 gives y = 1.4.

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