Posted by
Anjali Kaur
on
Jul 06, 2021
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.
Feel free to join our Facebook group.
A quick note: Subscribe to our website to get answers to your curriculum questions. You can also subscribe to our YouTube channel.
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
Thank You!
Feel free to join our Facebook group and subscribe to this website to get daily educational content in your mailbox.
Happy Learning!
Disclosure: Some of the links on the website are ads, meaning at no additional cost to you, I will earn a commission if you click through or make a purchase.
Comments are closed.
