Total divided by number

The idea

The average or Arithmetic Mean (A.M.), or simply mean, is Mean = Sum of all the values in the data ÷ Number of values in the data.

Flowers in the garden

Vaishnavi counts the hibiscus flowers that bloom in her garden each day: 2, 7, 9, 4, 3. The total is 25 flowers in 5 days.

If the same number of flowers bloomed every day, with the same total, how many would it be?

• 3 flowers
• 5 flowers
• 9 flowers

Share the heap equally

Pour all the days into one heap. Then deal the heap out equally to the days. Find the share that leaves nothing over and nothing missing.

Sum, then share

The heap is the sum of all the values. Dealing it out equally to all the days gives each day the same number. That number is the mean, also called the average.

The mean of Yashasvi’s runs is higher: 24 runs a match against 22.

The average or Arithmetic Mean (A.M.), or simply mean, is Mean = Sum of all the values in the data ÷ Number of values in the data.

• Data | Sum ÷ number | Mean
• 2, 7, 9, 4, 3 | 25 ÷ 5 | 5
• Shubman: 110 runs, 5 matches | 110 ÷ 5 | 22
• Yashasvi: 96 runs, 4 matches | 96 ÷ 4 | 24

Notes

The average or Arithmetic Mean (A.M.), or simply mean, is Mean = Sum of all the values in the data ÷ Number of values in the data.

Check yourself

Find the mean of 4, 8 and 6.

Answer: 6

4 + 8 + 6 = 18 and 18 ÷ 3 = 6.

Find the mean of 10, 20, 30 and 40.

Answer: 25

10 + 20 + 30 + 40 = 100 and 100 ÷ 4 = 25.

Shubman scored 110 runs in 5 matches. Yashasvi scored 96 runs in 4 matches. Whose average runs per match is higher?

The mean of 4 numbers is 8. What is the sum of the four numbers?

Answer: 32

Each of the 4 numbers can be thought of as 8, so the sum is 4 × 8 = 32.

• Yashasvi: 96 ÷ 4 = 24 against 110 ÷ 5 = 22 — correct. Yes! The mean fixes the problem of different numbers of matches.
• Shubman, because 110 is more than 96. That compares totals. The mean divides each total by its own number of matches.
• Both are the same. 110 ÷ 5 = 22 and 96 ÷ 4 = 24. They are different.