GROUP 3
THE WEIGHTED MEAN AND WORKING WITH GROUPED DATA
DEFINITION:
The weighted mean is a type of mean that is calculated by multiplying the weight (or
probability) associated with a particular event or outcome with its associated quantitative
outcome and then summing all the products together. It is very useful when calculating a
theoretically expected outcome where each outcome shows a different probability of
occurring.
The weighted mean is relatively easy to find. But in some cases, the weights might not add up
to 1. In those cases, you will need to use the weighted mean formula.
Formula:
Weighted mean =
This implies that Weighted Mean =
Where;
∑ denotes the sum
W is the weights
X is the value
In cases where the sum of weights is 1,
Weighted mean =
Calculation of Weighted Mean (Step by Step)
 Step 1: List the numbers and weights in tabular form.
 Step 2: Multiply each number and relevant weight assigned to that number
(w1*x1, w2* x2 ,…)
 Step 3: Add the numbers obtained in Step 2 (∑x1w1)
 Step 4: Find the sum of the weights (∑w1)
 Step 5: Divide the total of the values obtained in Step 3 by the sum of the
weights obtained in Step 4 (∑x1w1/∑w1)
In the case where the result in Step 4 is 1, then the sum of the values obtained in
Step 3 will be the weighted mean.
Worked example;
Numbers
Weights
7
3
10
4
5
7
11
10
8
5
Calculate for the weighted mean.
Solution;
Weighted mean =
=
=
=
=8.48
Therefore, the weighted mean is 8.48
CALCULATING FOR WEIGHTED MEAN USING EXCEL
Steps:
1. Draw a table with two columns with one column containing points and the
other containing their weights.
Activity
Points
Weight (%)
Assignment
87
10%
Project
92
20%
Recitation
95
15%
Quizzes
88
5%
Major Tests
93
30%
Final Exams
91
20%
2. Calculate for the SUM of weights in another cell.
(=SUM(C3,C4,C5,C6,C7,C8)
Activity
Assignment
Project
Recitation
Quizzes
Major Tests
Final Exams
Points
87
92
95
88
93
91
Using SUM:
Weight (%)
10%
20%
15%
5%
30%
20%
100%
3. Calculate the SUMPRODUCT (multiply each point by its weight and then
calculate their sum in order to get the sum product.)
(=SUMPRODUCT(B3:B8,C3:C8)
Activity
Assignment
Project
Recitation
Quizzes
Major Tests
Final Exams
Points
87
92
95
88
93
91
Weight (%)
10%
20%
15%
5%
30%
20%
Using SUM:
Using SUMPRODUCT:
100%
91.85
4. Now calculate for the weighted mean by dividing the SUMPRODUCT by the
SUM of the weights and press ENTER to get the result.
(=C12/C11)
Activity
Assignment
Project
Recitation
Quizzes
Major Tests
Final Exams
Points
87
92
95
88
93
91
Using SUM:
Using SUMPRODUCT:
WEIGHTED MEAN:
Weight (%)
10%
20%
15%
5%
30%
20%
100%
91.85
91.85
Therefore, the weighted mean is 91.85
WORKING WITH GROUPED DATA
Definition:
Grouped data is a type of data which is classified into groups after collection. The
raw data is classified into various groups and a table is created. The purpose of
the table is to show the data points occurring in each group. For instance, when a
quiz is conducted, the results are the data in this scenario and there are many
ways to group this data.
1. The number of students that scored above 15marks in the quiz can be
recorded and the number students who scored below 15marks can be
recorded.
2. The results can be recording in grades. For example, 15-20 is A and 0-5 is E.
Frequency table and histograms are best used to show and interpret
grouped data.
CALCULATING WEIGHTED MEAN USING GROUPED DATA
 The weighted mean computation can be used to obtain
approximations of the mean, variance, and standard deviation for
the grouped data.
 To compute the weighted mean, we treat the midpoint of each class
as though it were the mean of all items in the class.
 We compute a weighted mean of the class midpoints using the class
frequencies as weights.
 Similarly, in computing the variance and standard deviation, the class
frequencies are used as weights.
Example.
In a study of diabetic patients in a village, the following observations were
noted. Find the mean.
Ages
Number of patients
15 - 25
3
25 - 35
6
35 - 45
13
45 - 55
20
55 - 65
10
65- 75
5
Solution;
Ages
15 - 25
25 - 35
35 - 45
45 - 55
55 - 65
65- 75
TOTAL
Number of patients(f) Midpoint(x) fx
3
20
60
6
30
180
13
40
520
20
50
1000
10
60
600
5
70
350
57
2710
Mean =
=
=47.54385965
Therefore, the mean is 47.54385965
̅
̅
̅
midpoint(x)
(
3
20
-27.5
756.25
2268.75
6
30
-17.5
306.25
1837.5
13
40
-7.5
56.25
731.25
20
50
2.5
6.25
125
10
60
12.5
156.25
1562.5
5
70
22.5
506.25
2531.25
Number
of
patients(f)
TOTAL
57
Variance =
=
=
= 161.72
̅
9056.25
REFERENCES:
1. Basic statistics for business and economics (9th edition) LIND MARCHAL WATHEN
2. Statistics for business and economics (8th edition) Paul Newbold, William L. Carlson,
Betty M. Thorne