Jaspreet recently learnt cycling. She has explored different routes in her town. She tracked how much time she cycled on weekdays over the last 3 weeks. Find the mean time spent cycling per weekday over the last 3 weeks.
Step-by-step solution
| Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Weekly Average | |
|---|---|---|---|---|---|---|
| Week 1 | 10 | 13 | 10 | 15 | 16 | 12.8 |
| Week 2 | 14 | 10 | 20 | 17 | 18 | 15.8 |
| Week 3 | 15 | 18 | 14 | 20 | 23 | 18 |
To find: The mean cycling time per weekday over all 15 weekdays
Idea: Mean per weekday = total minutes ÷ number of weekdays (3 × 5 = 15). A weekly total is weekly average × 5. Since all weeks have the same number of days, the simple average of the weekly averages also works.
- Weekly totals (weekly average × 5): Week 1: 12.8 × 5 = 64; Week 2: 15.8 × 5 = 79; Week 3: 18 × 5 = 90 minutes. (Adding the table rows gives the same: 10 + 13 + 10 + 15 + 16 = 64, and so on.)1 mark
- Total time = 64 + 79 + 90 = 233 minutes over 5 + 5 + 5 = 15 weekdays.½ mark
- Mean time per weekday = 23315 = 15.53 minutes (to 2 decimal places).1 mark
- Quicker way, since every week has 5 days: 12.8 + 15.8 + 183 = 46.63 = 15.53 minutes, the same answer.½ mark
Check: 15.53 lies between the smallest weekly average (12.8) and the largest (18) ✓. Shortcut: 12.8 + 15.8 + 18 = 46.6 and 46.6 ÷ 3 = 15.53 ✓.
Answer to write in the exam
Total time in Week 1 = 12.8 × 5 = 64 min, Week 2 = 15.8 × 5 = 79 min, Week 3 = 18 × 5 = 90 min
Total time = 64 + 79 + 90 = 233 min; number of weekdays = 15
Mean time = 23315 = 15.53 min
∴ Mean time spent cycling per weekday = 15.53 minutes
Common mistakes that cost marks
- Dividing the total 233 by 3 (weeks) instead of 15 (weekdays).
- Adding the ‘Weekly Average’ column into the sum along with the daily times (e.g. 10 + 13 + 10 + 15 + 16 + 12.8), which counts that week twice.
- Using the shortcut ‘average of averages’ when the weeks have different numbers of days. It works here only because every week has 5 days.
How this can come in the exam
A shop’s average daily sales were ₹400 over 6 days in week 1 and ₹500 over 6 days in week 2. Its average daily sales over the 12 days were
- ₹450
- ₹900
- ₹454.50
- ₹445
Show answer
(A) ₹450
Equal numbers of days, so the average is 400 + 5002 = ₹450 (check: 2400 + 300012 = 450).
Rohan read for 4 days with an average of 30 minutes a day, and then for 6 days with an average of 40 minutes a day. Find his mean reading time per day over the 10 days.
Show answer
Totals: 4 × 30 = 120 min and 6 × 40 = 240 min (1 mark). Mean = 120 + 24010 = 36 minutes per day (1 mark). (Averaging 30 and 40 to get 35 would be wrong: the groups have different sizes.)Try one yourself
A batter played 3 tournaments of 4 matches each. Her average runs per match in them were 32, 40 and 45. Find her average runs per match over all 12 matches.
Show answer
Equal sizes, so 32 + 40 + 453 = 39 runs. Check: 128 + 160 + 18012 = 46812 = 39 ✓.
More questions like this
- We saw earlier how Method 1 (badminton example) did not produce the correct value. Why does Method 1 give the correct answer in this case? When does Method 1 work and when does it not work?
- Two glasses of equal quantities of lemonade are prepared. One glass has 10% jaggery and the other has 20% jaggery. If we mix the lemonade from both glasses, what is the concentration of jaggery in the mixture?
- A bowl of 500 mL lemonade has 10% jaggery. A glass of 200 mL lemonade has 20% jaggery. If we mix the lemonade from the bowl and the glass, what is the concentration of jaggery in the mixture?
Can you estimate what part of the mixture is jaggery? Is it 15%, or is it more or less? Why do you think so? - Brass is an alloy of copper and zinc. Batch A of brass weighs 200 kg of which 70% is copper. Batch B weighs 120 kg of which 50% is copper. Batch C is 45% copper. When all three batches are combined, we get an alloy that is 55% copper. What is the weight of Batch C?
- The average score of students on a test in Section A is 72 and that of students in Section B is 76. What is the combined average of both the sections given that Section A has 30 students and Section B has 25 students?