The average rainfall per day in the months of May, June, and July in a certain location are 3.5 mm, 10 mm and 8.7 mm respectively. Write an expression that gives their combined average.
Step-by-step solution
To find: An expression for the average rainfall per day over the three months
Idea: Each monthly average must be weighted by the number of days in that month, because the months are not of the same length.
- Total rainfall in each month = average × days: May 3.5 × 31, June 10 × 30, July 8.7 × 31 (in mm).½ mark
- Combined average = total rainfalltotal days = 3.5 × 31 + 10 × 30 + 8.7 × 3131 + 30 + 31.1 mark
- Its value: 108.5 + 300 + 269.792 = 678.292 ≈ 7.37 mm per day.½ mark
Check: The simple mean 3.5 + 10 + 8.73 = 7.4 is very close, because the months are almost the same length; the exact weighted answer 7.37 is slightly lower since June (the wettest) has one day fewer ✓.
Answer to write in the exam
Days: May = 31, June = 30, July = 31
Combined average = 3.5 × 31 + 10 × 30 + 8.7 × 3131 + 30 + 31
= 678.292 ≈ 7.37
∴ Combined average ≈ 7.37 mm per day
Common mistakes that cost marks
- Writing 3.5 + 10 + 8.73 without noticing that June has 30 days while May and July have 31.
- Taking June as 31 days or July as 30 days.
- Dividing by 3 (months) in the weighted expression instead of by 92 (days).
How this can come in the exam
The average daily temperature was 25 °C over a 30-day month and 31 °C over the next 30-day month. The average daily temperature over the two months was
- 28 °C
- 56 °C
- 27.5 °C
- 28.5 °C
Show answer
(A) 28 °C
Equal numbers of days: 25 × 30 + 31 × 3060 = 25 + 312 = 28 °C.
Try one yourself
The average daily rainfall in February (28 days) is 2 mm and in March is 4 mm. Write the expression for the combined average and evaluate it.
Show answer
2 × 28 + 4 × 3128 + 31 = 56 + 12459 = 18059 ≈ 3.05 mm per day.
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