In this publication, we will consider what the arithmetic mean of numbers (two, three, four, etc.) is, we will give a formula with which it can be found, and we will also analyze examples of problems for a better understanding of theoretical material.
Definition and formula
Average two or more numbers is the ratio of their total to their number. Calculated as follows:
- a1, a2,…, an-1 и an – numbers (or terms);
- n is the number of all terms.
Special cases of the formula:
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Note: The Greek letter is usually used to denote the arithmetic mean. μ (read as “mu”).
Examples of tasks
Task 1
Petya had 4 apples, Dasha had 6, and Lena had 5. They decided to put all the fruits together and divide them equally among each. Calculate how many apples each will get.
Solution
In this case, we have three numbers, and we need to find their arithmetic mean. To do this, use the above formula:
Answer: each gets 5 apples.
Task 2
The athlete spent 5 hours covering the distance from point A to point B, while his speed was as follows: the first two hours – 6 km/h, then two hours – 9 km/h, and the last 60 minutes – 7 km/h. Find your average speed.
Solution
So, we need to calculate the arithmetic average of five numbers that correspond to speeds for each hour of running:
Answer: the average speed of an athlete is 7,4 km/h.