Using the mean

The mean is worth practising on real data, because reading the answer takes as much care as computing it.

Shreyas bounces a ball on a bat, counting how many times before it falls. Over 8 attempts he gets 6, 2, 9, 5, 4, 6, 3, 5.

Add them: 6 + 2 + 9 + 5 + 4 + 6 + 3 + 5 = 40. Divide by the number of attempts: 40 ÷ 8 = 5. On average he manages 5 bounces. Try the activity yourself with 7 or more attempts.

Vaishnavi tracks Hibiscus flowers blooming in her garden: 2, 7, 9, 4, 3 over five days. The mean is (2 + 7 + 9 + 4 + 3) ÷ 5 = 25 ÷ 5 = 5. On average, 5 flowers bloom daily — that is, the number that would bloom each day if the same number bloomed every day.

Now a comparison where the meaning of 'better' flips. Two friends train for a 100 m race. Nikhil's times, in seconds, are 17, 18, 17, 16, 19, 17, 18. Sunil's are 20, 18, 18, 17, 16, 16, 17. Who on average ran quicker?

Nikhil's total is 122 over 7 runs, so his mean is about 17.43 seconds. Sunil's total is 122 over 7 runs too, so his mean is also about 17.43 seconds. Their averages are identical — so on average neither ran quicker, though their patterns differ. And note that for a race, a SMALLER mean time is the better performance, unlike runs scored.

One more. A school's enrolment over six consecutive years was 1555, 1670, 1750, 2013, 2040, 2126. The total is 11154, so the mean enrolment is 11154 ÷ 6 = 1859.