A white stork’s migration is tracked. The average daily distance travelled, calculated over 20 days, is 44.5 km. On the 21st day, it flew 55 km. What is the average daily distance travelled over these 21 days? Make a guess before you calculate.
Step-by-step solution
To find: Average daily distance over 21 days
Idea: One new value is a ‘collection’ of size 1. The new average is the weighted mean of the old average (weight 20) and the new value (weight 1).
- Guess: 55 is above 44.5, so the average will rise, but only a little, because one day counts against twenty. Expect about 45 km.½ mark
- Distance in the first 20 days = 20 × 44.5 = 890 km. Total over 21 days = 890 + 55 = 945 km.1 mark
- Average = 94521 = 45 km per day.½ mark
Check: 21 × 45 = 945 ✓. The rise is 55 − 44.521 = 0.5 km, as expected for one higher day ✓.
Answer to write in the exam
Distance in 20 days = 20 × 44.5 = 890 km
Distance in 21 days = 890 + 55 = 945 km
Average = 94521 = 45
∴ Average daily distance over 21 days = 45 km
Common mistakes that cost marks
- Averaging 44.5 and 55 to get 49.75 km. The 44.5 stands for 20 days, the 55 for only 1.
- Dividing 945 by 20 instead of 21.
- Skipping the guess. The question asks for an estimate first.
How this can come in the exam
The average of 10 numbers is 20. An 11th number, 31, is added. The new average is
- 21
- 25.5
- 20.5
- 22
Show answer
(A) 21
200 + 3111 = 23111 = 21.
A batter’s average over 15 innings is 40 runs. How many runs must she score in the 16th innings to raise her average to 42?
Show answer
Runs needed in total = 16 × 42 = 672; runs so far = 15 × 40 = 600 (1 mark). Runs needed = 672 − 600 = 72 (1 mark).Try one yourself
Arun’s average over 9 days is 8000 steps a day. On the 10th day he walks 13000 steps. Find his new average.
Show answer
9 × 8000 + 1300010 = 8500010 = 8500 steps a day.
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