The Average: One Number For A Whole Group

Use the mean to compare groups of different sizes, and see it as the fair share when everything is shared equally.

9 micro-lessons

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Balancing Highs and Lows

The mean: total of all values ÷ number of values.

	M1	M2	M3	M4	M5
Shubman	23	07	10	52	18
Yashasvi	26	53	02	–	15

Yashasvi did not bat in match 4.

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Using the mean to settle both batting arguments.

Problem. Who batted better in each series? (Textbook pp. 98–99)

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Mean = sum of all values ÷ number of values.

Average or Arithmetic Mean (Textbook p. 100)

Mean = \frac{Sum of all the values in the data}{Number of values in the data}

What each part means

sum

— add every value

number

— count how many values there are

When it works

Works for any list of numbers. The mean need not be one of the values.

Example

Bounces 6, 2, 9, 5, 4, 6, 3, 5:

40 \div 8 = 5

Use the mean to compare batters.

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First series: Shubman 0, 17, 21, 90. His mean?

If everyone shared equally, each would get the mean.

Shreyas and 4 friends collected 3, 8, 10, 5 and 4 guavas. Parag and 5 friends collected 5, 4, 6, 3, 4 and 8. Each group shares its guavas equally.

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Finding the average number of flowers blooming per day.

Problem. Vaishnavi counted hibiscus flowers blooming in her garden on 5 days: 2, 7, 9, 4, 3. What is the average per day? (Textbook pp. 100–101)

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The book's Figure it Out problems on the mean.

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Shreyas bounces a ball on a bat 6, 2, 9, 5, 4, 6, 3, 5 times in 8 attempts. Average? (Textbook p. 101, Q1)