In calculation of weighted median, the importance of all the items was considered to be equal. However, there may be situations in which all the items under considerations are not equal importance. For example, we want to find average number of marks per subject who appeared in different subjects like Mathematics, Statistics, Physics and Biology. These subjects do not have equal importance. Learning the formula to find weighted median by giving Median.
Learning Median Definition:
The arithmetic median computed by specific importance of every object is known weighted arithmetic median. To consider the every importance object, we can assume number known as weight to every object is directly proportional to its specific importance.
Weighted Arithmetic Median is computed by using following formula:
`sum` Yw = `(sum ty) / (sum t)`
Where:
Yw Stands for weighted arithmetic median.
y Stands for values of the items and
t Stands for weight of the item
Learning the important three methods of weighted median:
1.Arithmetic Median
2. Weighted Average
3. Average speed.
The formula for weighted average is:
Weighted Average = Sum of weighted objects / total number of objects
Learning to solve examples of Weighted median:
Ex 1:A student obtained 30, 40, 50, 60, and 35 marks in the subjects of Math, Statistics, Physics, Chemistry and Biology respectively. Assuming weights 1, 3, 5, 4, and 2 respectively for the above mentioned subjects. Find Weighted Arithmetic Mean per subject.
Solution:
Now we will find weighted arithmetic mean as:
`sum` Yw = `( sum ty)/(sum t) = 710/ 15` = 47.33marks/subject
Ex 2: A class of 30 students took a math test. 15 students had an average (arithmetic median) score of 90. The other students had an average score of 70. What is the average score of the whole class?
Solution:Step 1: To get the sum of weighted terms, multiply each average by the number of students that had that average and then sum them up.
90 × 15 + 70 × 15 = 1350 + 1050 = 2400
Step 2: Total number of objects = Total number of students = 30
Step 3: Using the formula
Weighted Average = Sum of Weighted objects / Total Numbers of objects.
= `2400 / 30`
= 80.
Answer: The average score of the whole class is 80.
Learning Median Definition:
The arithmetic median computed by specific importance of every object is known weighted arithmetic median. To consider the every importance object, we can assume number known as weight to every object is directly proportional to its specific importance.
Weighted Arithmetic Median is computed by using following formula:
`sum` Yw = `(sum ty) / (sum t)`
Where:
Yw Stands for weighted arithmetic median.
y Stands for values of the items and
t Stands for weight of the item
Learning the important three methods of weighted median:
1.Arithmetic Median
2. Weighted Average
3. Average speed.
The formula for weighted average is:
Weighted Average = Sum of weighted objects / total number of objects
Learning to solve examples of Weighted median:
Ex 1:A student obtained 30, 40, 50, 60, and 35 marks in the subjects of Math, Statistics, Physics, Chemistry and Biology respectively. Assuming weights 1, 3, 5, 4, and 2 respectively for the above mentioned subjects. Find Weighted Arithmetic Mean per subject.
Solution:
Subjects |
Marks Obtained
y |
Weight
t |
`sum` ty
|
| Math |
30
| 1 | 30 |
| Statistics | 40 | 3 | 120 |
| Physics |
50
|
5
| 250 |
Chemistry
|
60
|
4
|
240
|
Biology
|
35
| 2 | 70 |
Total
| `sum` t = 15 | `sum` y= 710 |
Now we will find weighted arithmetic mean as:
`sum` Yw = `( sum ty)/(sum t) = 710/ 15` = 47.33marks/subject
Ex 2: A class of 30 students took a math test. 15 students had an average (arithmetic median) score of 90. The other students had an average score of 70. What is the average score of the whole class?
Solution:Step 1: To get the sum of weighted terms, multiply each average by the number of students that had that average and then sum them up.
90 × 15 + 70 × 15 = 1350 + 1050 = 2400
Step 2: Total number of objects = Total number of students = 30
Step 3: Using the formula
Weighted Average = Sum of Weighted objects / Total Numbers of objects.
= `2400 / 30`
= 80.
Answer: The average score of the whole class is 80.
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