Everyone gets the same

The idea

The mean is a fair share or equal share: the value each member would have if the total were shared equally, or if all values were equal.

Two groups of guava pickers

Shreyas and 4 friends collected 30 guavas together. Parag and 5 friends also collected 30 guavas together. Each group will share its guavas equally among its members.

In which group will each member get the bigger share?

• Shreyas’s group (5 members)
• Parag’s group (6 members)
• Both get the same share

Level the columns

Each column is one friend’s guavas. Move one guava at a time from a column that has more to a column that has less, until all columns are the same.

Moving does not change the total

Moving guavas around never changed the total, 30. When everyone had the same number, that number was the fair share. It is the mean.

So 6 × 5 = 30 and 5 × 6 = 30. Shreyas’s friends each get 1 guava more.

Old Indian books gave this idea names such as samamiti: “sama” means equal.

The mean is a fair share or equal share: the value each member would have if the total were shared equally, or if all the values were equal.

• Group | Total | Members | Each gets
• Shreyas | 30 | 5 | 6
• Parag | 30 | 6 | 5

Notes

The mean is a fair share or equal share: the value each member would have if the total were shared equally, or if all the values were equal.

Check yourself

Four friends have 1, 4, 8 and 11 marbles. If they share all the marbles equally, how many does each get?

Answer: 6

1 + 4 + 8 + 11 = 24 marbles, and 24 ÷ 4 = 6 each.

An orchard has 5 trees. The mean number of mangoes per tree is 12. How many mangoes are there on all 5 trees?

Answer: 60

Each of the 5 trees stands for 12 mangoes: 5 × 12 = 60.

Both groups have 30 guavas. Why does each member of Shreyas’s group get more than each member of Parag’s?

The mean number of guavas in a group is 6. Does every member have 6 guavas?

• Shreyas’s group has fewer members to share among. — correct. Yes! The same total shared among 5 gives more than shared among 6.
• Shreyas’s group picked bigger guavas.. The size of the guavas is not the reason. The totals are the same, 30.
• Shreyas’s group has a bigger total.. Both totals are 30. The difference is the number of members.
• No. 6 is only what each would have after sharing equally. — correct. Yes! Real values can differ, like 3, 8 and 10. The mean is the equal-share value.
• Yes, every member has exactly 6.. In Shreyas’s group the members had 3, 8, 10, 5 and 4. Only after sharing do they all have 6.
• No, but everyone has at least 6.. Some members had fewer than 6. The mean lies between the smallest and the biggest value.