Answer:
To convert a grouped frequency distribution to a relative frequency distribution, you need to divide the frequency of each category by the total number of data points.
1. Calculate the total frequency by summing up all the frequencies in the grouped frequency distribution.
2. Create a new table or distribution with the same categories as the original grouped frequency distribution.
3. For each category, divide the frequency by the total frequency to obtain the relative frequency.
4. Multiply the relative frequency by 100 if you wish to express it as a percentage.
Original Grouped Frequency Distribution:
Category Frequency
0-10 12
10-20 20
20-30 15
30-40 8
40-50 5
Step 1: Calculate the total frequency:
Total frequency = 12 + 20 + 15 + 8 + 5 = 60
Step 2: Create a new table or distribution with the same categories:
Category Frequency Relative Frequency (%)
0-10 12 -
10-20 20 -
20-30 15 -
30-40 8 -
40-50 5 -
Step 3: For each category, divide the frequency by the total frequency to obtain the relative frequency:
Category Frequency Relative Frequency (%)
0-10 12 12/60 = 0.2 (20%)
10-20 20 20/60 = 0.33 (33%)
20-30 15 15/60 = 0.25 (25%)
30-40 8 8/60 = 0.13 (13%)
40-50 5 5/60 = 0.08 (8%)
Step 4: If desired, multiply the relative frequency by 100 to express it as a percentage:
Category Frequency Relative Frequency (%)
0-10 12 20%
10-20 20 33%
20-30 15 25%
30-40 8 13%
40-50 5 8%
The resulting table above is the relative frequency distribution.
Step-by-step explanation: