Weighted rate calculation - example

For more information on calculation method of rates in indicators, click here.

You want to calculate the rate of males and female adults and minors (numerator) for their corresponding population groups (denominator). The population may change over time.

Here's a general approach to calculating these rates:

Calculate the Rate for Each Gender:

Count the number of observations for each gender.
Calculate the weighted average denominator for each gender (sum of denominators for all observations in that gender, divided by the number of observations in that gender).
Calculate the rate for each gender (number of observations in the gender divided by the weighted average denominator for that gender).

Calculate the Rate for Each Age Group:

Count the number of observations for each age group.
Calculate the weighted average denominator for each age group.
Calculate the rate for each age group

Calculate the Overall Rate:

Count the total number of observations.
Calculate the total weighted average denominator (sum of all denominators divided by the total number of observations).
Calculate the overall rate (total number of observations divided by the total weighted average denominator).

Here is an example. Here is a dataset of 20 beneficiaries with information related to gender and age group. They are the participants surveyed during data collection. I want to know what is the rate (%) of participation on the overall population. The Denominator column is the population of the gender/age group at a specific period.

Participant	Age	Gender	Denominator	Period
ID01	<18	Male	100	Q1
ID02	>=18	Male	150	Q1
ID03	>=18	Female	120	Q1
ID04	<18	Female	80	Q1
ID05	<18	Female	100	Q1
ID06	>=18	Male	110	Q1
ID07	<18	Male	130	Q2
ID08	>=18	Male	140	Q2
ID09	>=18	Female	90	Q2
ID10	<18	Female	70	Q2
ID11	<18	Female	95	Q2
ID12	>=18	Male	115	Q2
ID13	<18	Male	105	Q3
ID14	>=18	Male	155	Q3
ID15	>=18	Female	125	Q3
ID16	<18	Female	85	Q3
ID17	<18	Female	105	Q3
ID18	>=18	Male	120	Q3
ID19	<18	Male	135	Q4
ID20	>=18	Male	160	Q4

Now, let's calculate the rates:

For Gender:
- Male Count = 11
- Female Count = 9
- Total Count (Gender) = 20
- Weighted Average Denominator for Males: 1420 / 11 = 129.09
- Weighted Average Denominator for Females: 870 / 9 = 96.67
- Total Weighted Average Denominator (Gender): (1420+870) / 20 =114.5

For Age:
- <18 Count = 10
- >=18 Count = 10
- Total Count (Age) = 20
- Weighted Average Denominator for <18: 1080 / 10 = 109
- Weighted Average Denominator for >=18: 1200/10 = 120
- Total Weighted Average Denominator (Age) = (1090+1200) / 20 = 114.5

For combined Gender/Age
- Count of Male <18 = 5
- Count of Male >=18 = 6
- Weighted Average Denominator for Male <18 = 126.0
- Weighted Average Denominator for Male >=18 = 131.67
- Count of Female <18 = 5
- Count of Female >=18 = 4
- Weighted Average Denominator for Female <18 = 92.0
- Weighted Average Denominator for Female >=18 = 102.5

Total rate:

Sum of all participants = 20
Sum of all denominators divided by the total count of participants = 114.5
Total rate: 20/114.5 = 0.1747 or 17.47%