The daily distance (in km) run by 50 autorickshaws in a town is: 40-60: 6, 60-80: 10, 80-100: 16, 100-120: 12, 120-140: 6. Find the mean distance by the step-deviation method.

1. 1 · Write what is given and what is to be found. Given: five classes of size 20; Σfᵢ = 50. To find: the mean distance.
2. 2 · Write the formula. x̄ = a + h × (Σfᵢuᵢ ÷ Σfᵢ), where uᵢ = (xᵢ − a) ÷ h.
3. 3 · Choose a and h, then make the table.
   • Class marks: 50, 70, 90, 110, 130. Take a = 90 and h = 20.
   • uᵢ: −2, −1, 0, 1, 2.
   • fᵢuᵢ: −12, −10, 0, 12, 12.
4. 4 · Add the columns. Σfᵢ = 50; Σfᵢuᵢ = −22 + 24 = 2.
5. 5 · Substitute. x̄ = 90 + 20 × (2 ÷ 50) = 90 + 0.8 = 90.8.
6. 6 · Check and box the answer. Σfᵢuᵢ is positive, so the mean is just above 90. Box: mean distance = 90.8 km.

Scoring tip: Write a and h above the table. Examiners look for both before they look at the answer.