how would you convert a grouped frequency distribution to a relative frequency distribution?
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.
Here are the steps to follow:
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.
Here's an example to illustrate the process:
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.
To convert a grouped frequency distribution to a relative frequency distribution, you need to follow these steps:
1. Calculate the total frequency by summing up all the frequencies in the grouped distribution.
2. Add an additional column to your table, which will represent the relative frequency. This column should be labeled "Relative Frequency."
3. For each class interval in the grouped frequency distribution, divide the frequency by the total frequency, and then multiply by 100 to get the relative frequency.
4. Record the calculated relative frequencies in the corresponding row of the new "Relative Frequency" column.
5. Remember to express the relative frequencies as percentages by adding a "%" symbol after the values.
By following these steps, you will convert a grouped frequency distribution to a relative frequency distribution.