The daily exercise time (in minutes) of 50 students is: 0-10: 6, 10-20: 9, 20-30: 15, 30-40: 12, 40-50: 8. Find the mean exercise time by the direct method.

1. 1 · Write what is given and what is to be found. Given: five classes with frequencies 6, 9, 15, 12, 8. To find: the mean x̄.
2. 2 · Write the formula. x̄ = Σfᵢxᵢ ÷ Σfᵢ, where xᵢ is the class mark.
3. 3 · Make the table.
   • Class marks xᵢ: 5, 15, 25, 35, 45.
   • fᵢxᵢ: 30, 135, 375, 420, 360.
4. 4 · Add the columns. Σfᵢ = 50; Σfᵢxᵢ = 30 + 135 + 375 + 420 + 360 = 1320.
5. 5 · Divide. x̄ = 1320 ÷ 50 = 26.4 minutes.
6. 6 · Say what it means. On average, a student exercises about 26.4 minutes a day.
7. 7 · Check and box the answer. 26.4 lies in the middle class 20-30, which has the most students, so it is sensible. Box: x̄ = 26.4 minutes.

Scoring tip: Draw the table with ruled columns and write the totals in a last row. A correct table earns marks on its own.