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Mean by the assumed mean method sheet
3-mark answer frame

The weights (in grams) of 40 tomatoes are: 50-60: 4, 60-70: 8, 70-80: 14, 80-90: 10, 90-100: 4. Find the mean weight by the assumed mean method.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found. Given: five classes, Σfᵢ = 40. To find: the mean weight by the assumed mean method.
  2. 2 · Write the formula. x̄ = a + Σfᵢdᵢ ÷ Σfᵢ, where dᵢ = xᵢ − a.
  3. 3 · Choose a and make the table.
    • Class marks: 55, 65, 75, 85, 95. Take a = 75.
    • dᵢ: −20, −10, 0, 10, 20.
    • fᵢdᵢ: −80, −80, 0, 100, 80.
  4. 4 · Add the columns. Σfᵢ = 40; Σfᵢdᵢ = −160 + 180 = 20.
  5. 5 · Substitute. x̄ = 75 + 20 ÷ 40 = 75 + 0.5 = 75.5.
  6. 6 · Check and box the answer. Σfᵢdᵢ is positive, so the mean is a little more than 75. Box: mean weight = 75.5 g.

Scoring tip: Write 'a = 75' clearly above the table. Keep every minus sign in the dᵢ and fᵢdᵢ columns.