# 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 a

_{1}, a_{2}, ... ,a_{n}, then the arithmetic mean**A**is defined by the formulaA = | a_{1} + a_{2} + ... + a_{n} |

n |

For example:

for two numbers

for three numbers

and so on.

for two numbers

a

and b

**is***arithmetic mean*a + b |

2 |

for three numbers

a

, b

and c

**is***arithmetic mean*a + 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:4 + 2 + 6 | = | 12 | = 4 |

3 | 3 |

**Answer:**each got**4**pears.
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:15 + 10 + 12 + 11 + 7 + 14 + 8 | = | 77 | = 11 |

7 | 7 |

**Answer:**an average programming courses visit**11**people a day.
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:120 + 120 + 90 | = | 330 | = 110 |

3 | 3 |

**Answer:**the average speed of the car wos**110**km/h.
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.

So the sum of all 10 numbers is equal to 18 + 21 = 39, and arithmetic mean is equal to

**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 |

**Answer:**arithmetic mean of 10 numbers is equal to**3.9**.*Add the comment*