To find the mean of age grouped data, you calculate a weighted average using the midpoints of each age group and their corresponding frequencies. Here's a step-by-step breakdown:
1. Determine the Midpoint (Class Mark) for Each Group
The midpoint of each age group (or class interval) is calculated by averaging the upper and lower limits of that group.
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Formula: Midpoint = (Upper Limit + Lower Limit) / 2
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Example: If you have an age group of 20-29, the midpoint would be (20 + 29) / 2 = 24.5
2. Multiply Each Midpoint by its Frequency
The frequency represents the number of individuals within each age group. Multiply the midpoint you calculated in the previous step by the frequency of that age group. This gives you a weighted value for each group.
- Example: If the age group 20-29 (midpoint 24.5) has a frequency of 15, then the product would be 24.5 * 15 = 367.5
3. Sum the Products
Add up all the products calculated in step 2. This gives you the total weighted value of all the age groups.
4. Divide the Sum by the Total Frequency
Divide the sum of the products (from step 3) by the total number of observations (i.e., the sum of all the frequencies). This gives you the mean of the age grouped data.
- Formula: Mean = (Sum of (Midpoint * Frequency)) / (Sum of Frequencies)
Example
Let's say we have the following age grouped data:
| Age Group | Frequency |
|---|---|
| 10-19 | 10 |
| 20-29 | 15 |
| 30-39 | 20 |
| 40-49 | 5 |
Calculations:
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Midpoints:
- 10-19: (10 + 19) / 2 = 14.5
- 20-29: (20 + 29) / 2 = 24.5
- 30-39: (30 + 39) / 2 = 34.5
- 40-49: (40 + 49) / 2 = 44.5
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*Midpoint Frequency:**
- 14.5 * 10 = 145
- 24.5 * 15 = 367.5
- 34.5 * 20 = 690
- 44.5 * 5 = 222.5
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*Sum of (Midpoint Frequency):** 145 + 367.5 + 690 + 222.5 = 1425
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Total Frequency: 10 + 15 + 20 + 5 = 50
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Mean: 1425 / 50 = 28.5
Therefore, the mean age of this grouped data is 28.5.
Summary
Calculating the mean of age-grouped data involves determining the midpoint of each group, multiplying it by its frequency, summing these products, and then dividing by the total frequency. This process effectively estimates the average age within the population represented by the grouped data.
