Arithmetic mean
Definition. The arithmetic mean of several numbers is the ratio of the sum of all this numbers to their total number.
| Arithmetic mean = | sum of numbers |
| total number |
Arithmetic mean formula.
If we have a data set containing the values a1, a2, ... ,an , then the arithmetic mean A is defined by the formula
| A = | a1 + a2 + ... + an |
| n |
For example:
for two numbers
for three numbers
and so on.
for two numbers
a
and b
arithmetic mean isa + b |
| 2 |
for three numbers
a
, b
and c
arithmetic mean isa + b + c |
| 3 |
and so on.
Examples of tasks with arithmetic mean
Example 1. Bob plucked from the tree 4 pears, Kate - 2 pears, and John - 6. Children fruits piled together and divided equally. How many pears got each of them?
Solution. Find the arithmetic mean:
Answer: each got 4 pears.
Solution. Find the arithmetic mean:
| 4 + 2 + 6 | = | 12 | = 4 |
| 3 | 3 |
Example 2. On programming courses 15 people came on Monday, 10 on Tuesday,12 on Wednesday, 11 on Thursday, 7 on Friday, 14 on Saturday, 8 on Sunday. Find the mean attendance of courses for the week.
Solution. Find the arithmetic mean:
Answer: an average programming courses visit 11 people a day.
Solution. Find the arithmetic mean:
| 15 + 10 + 12 + 11 + 7 + 14 + 8 | = | 77 | = 11 |
| 7 | 7 |
Example 3. The driver drove two hours at a speed of 120 km/h and hour at a speed of 90 km/h. Find the average speed of the car.
Solution. Let us find arithmetic mean of car speeds for each hour of the way:
Answer: the average speed of the car wos 110 km/h.
Solution. Let us find arithmetic mean of car speeds for each hour of the way:
| 120 + 120 + 90 | = | 330 | = 110 |
| 3 | 3 |
Example 4. Arithmetic mean of 3 numbers is equal to 6, and arithmetic mean of other 7 numbers is equal to 3. Find the arithmetic mean of all 10 numbers.
Solution. Since arithmetic mean of 3 numbers is equal to 6 then their sum is equal to 6 · 3 = 18, similar the sum of remaining 7 numbers is equal to 7 · 3 = 21.
So the sum of all 10 numbers is equal to 18 + 21 = 39, and arithmetic mean is equal to
Answer: arithmetic mean of 10 numbers is equal to 3.9.
Solution. Since arithmetic mean of 3 numbers is equal to 6 then their sum is equal to 6 · 3 = 18, similar the sum of remaining 7 numbers is equal to 7 · 3 = 21.
So the sum of all 10 numbers is equal to 18 + 21 = 39, and arithmetic mean is equal to
| 39 | = 3.9 |
| 10 |
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