# Calculating Weighted Arithmetic Mean

Under weighted arithmetic mean, sometimes we may give greater significance to some items and less to others. In the case of working women; the priorities are different, family will be given more importance, then work, then health, or leisure. In such cases, calculating weighted arithmetic mean becomes important. Let’s learn this.

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## The formula for Weighted Arithmetic Mean

Steps involved:

- Find the total of weights.
- Find weight multiplied by the items.

Let’s try some questions for a better understanding.

## Solved Questions

- Calculate the weighted mean of the following data:

Items (X) | 5 | 10 | 25 | 20 | 25 | 30 |

Weights (w) | 8 | 4 | 5 | 10 | 7 | 6 |

Solution:

Recreate this table in a vertical manner for better understanding;

Items (X) | Weights (w) | XW |
---|---|---|

5 | 8 | 40 |

10 | 4 | 40 |

25 | 5 | 125 |

20 | 10 | 200 |

25 | 7 | 175 |

30 | 6 | 180 |

40 | 760 |

Following 2 simple steps;

Summation of weight = 40

Summation of items by weight = 760

Applying the following formula:

= 760/40 = 19

Let’s try another question.

2. The following table shows prices per 100g of tea of different brands. Using quantities as weight, find out the weighted arithmetic mean of the prices.

Price per 100 g | 2.5 | 3 | 3.5 | 4 | 4.25 | 5 |

Quantity | 10 | 8 | 8 | 4 | 4 | 2 |

Solution.

Arrange the given table in vertical form.

Price per 100 g (X) | Quantity (W) | XW |
---|---|---|

2.5 | 10 | 25 |

3 | 8 | 24 |

3.5 | 8 | 28 |

4 | 4 | 16 |

4.25 | 4 | 17 |

5 | 2 | 10 |

36 | 120 |

Using the simple 2 steps and applying the below formula:

Summation of weight = 36

Summation of weight by item = 120

= 120/36 = 3.33

## Try understanding via my tutorial.

In this video, I have explained a different question on the weighted arithmetic mean.

## Test Yourself

- Calculate the weighted mean of the following data:

Marks (X) | 81 | 76 | 74 | 58 | 70 | 73 |

Weight (w) | 2 | 3 | 6 | 7 | 3 | 7 |

**(Answer – 70.04)**

2. Calculate the weighted mean of the following data:

Marks | 60 | 75 | 63 | 59 | 55 |

Weight | 2 | 1 | 5 | 5 | 3 |

**(Answer – 60.625)**

3. Calculate the weighted mean of the following data:

Items | 96 | 102 | 104 | 124 | 148 | 164 |

Weight | 5 | 6 | 3 | 7 | 12 | 9 |

**(Answer – 131.52)**

4. A student obtained 60 marks in English, 75 in Hindi, 63 in Maths, 59 in Economics, and 55 in Statistics. Calculate the weighted mean of the marks if weights are respectively 2,1,5,5 and 3.

**(Answer – 60.625)**

I hope it was helpful, you can refer to more posts related to the statistics.

- Individual Series Arithmetic Mean
- Discrete Series Arithmetic Mean
- Continuous Series Arithmetic Mean
- Inclusive and Exclusive Series – Arithmetic mean
- Introduction to the statistics.
- Functions and importance of statistics.
- Calculating Correct Arithmetic mean

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