Certainly! Let's dive into the details of how to calculate the frequency distribution and relative frequency for an age group.

1. Frequency Distribution

A frequency distribution is a summary of how often each value or range of values occurs in a data set. When dealing with age groups, the steps are as follows:

Steps to Calculate Frequency Distribution for Age Groups:

1. Collect Data: Gather the age data of individuals. This could be a list of ages from a survey or a database.

2. Determine Age Groups: Decide on the age groups (also called intervals or bins) that you want to use. For example, you might choose:

   • 0-10 years
   • 11-20 years
   • 21-30 years
   • etc.

3. Tally the Ages: Go through the age data and count how many individuals fall into each age group.

4. Create the Frequency Table: List the age groups and next to each group, write down the tally (count) of how many individuals fall into that group. This list is your frequency distribution.

Example:

Assume we have the following ages: 12, 23, 35, 42, 55, 21, 17, 33, 45, 28, 34, 19, 22.

Age Groups	Frequency
0-10	0
11-20	4
21-30	5
31-40	2
41-50	2
51-60	1

2. Relative Frequency

Relative frequency shows how often something happens relative to the total number of observations. It's essentially the proportion of the total that each age group represents.

Steps to Calculate Relative Frequency:

1. Calculate Total Frequency: Add up all the frequencies from your frequency distribution. This gives you the total number of observations.

2. Calculate Relative Frequency: For each age group, divide its frequency by the total frequency. This gives you the relative frequency.

3. Convert to Percentage (Optional): Multiply the relative frequency by 100 to express it as a percentage.

Example:

Continuing from the frequency distribution above, suppose the total number of observations (total frequency) is 14.

• For the 11-20 age group:

  • Frequency = 4
  • Total Frequency = 14
  • Relative Frequency = 4/14 ≈ 0.286 (or 28.6%)

  Repeat this calculation for each age group.

Summary Table:

Age Groups	Frequency	Relative Frequency (%)
0-10	0	0.0%
11-20	4	28.6%
21-30	5	35.7%
31-40	2	14.3%
41-50	2	14.3%
51-60	1	7.1%

Why Use Frequency Distribution and Relative Frequency?

• Frequency Distribution helps you understand how data is spread across different intervals.
• Relative Frequency gives insight into the proportion of each interval, which is useful when comparing groups of different sizes.

Do You Want Details or Have Any Questions?

5 Related Questions:

1. How do you decide the width of each age group (bin size)?
2. Can you explain cumulative frequency and how it differs from regular frequency?
3. How would you create a histogram from the frequency distribution?
4. What are some common pitfalls when interpreting frequency distributions?
5. How can you use frequency distribution in data analysis?

Tip:

When choosing age groups, ensure that the intervals are of equal width to make comparison easier and more meaningful.