Learning outcomes
- define frequency distribution
- build a frequency table for categorical data
- compute relative frequency and percentage
- interpret the most common category correctly
What is a frequency distribution?
- A frequency distribution shows how often each category occurs.
- It is one of the simplest ways to summarize categorical data.
CSE, ECE, CSE, ME, CSE, ECE, CE, CSE
| Branch | Frequency |
|---|---|
| CSE | 4 |
| ECE | 2 |
| ME | 1 |
| CE | 1 |
Why frequency distributions matter
- They reduce messy raw data into a usable summary.
- They help identify:
- most common category
- least common category
- distribution pattern
Relative frequency
- Relative frequency tells what proportion of observations fall in each category.
relative frequency = category frequency / total frequency
- total =
8 - for
CSE, relative frequency =4/8 = 0.5
Percentage distribution
- Percentage gives relative frequency in percent form.
percentage = relative frequency x 100
CSE = 0.5 x 100 = 50%
Complete table format
| Category | Frequency | Relative Frequency | Percentage |
|---|---|---|---|
| CSE | 4 | 0.50 | 50% |
| ECE | 2 | 0.25 | 25% |
| ME | 1 | 0.125 | 12.5% |
| CE | 1 | 0.125 | 12.5% |
Things to check in a correct table
- all categories are included
- category labels are clear
- frequencies add to total
- relative frequencies add to
1 - percentages add to
100%apart from rounding differences
Exam hints and traps
- Frequency is count, not percentage.
- Relative frequency is not written as raw count.
- Percentages may sum to
99.9%or100.1%due to rounding. - The “most frequent” category is the mode.
Quick practice
Raw responses:A, B, A, C, A, B, D, B, A, C
- Construct a frequency table.
- Find the relative frequency of
B. - Which category is the mode?
Answer key
-
A = 4,B = 3,C = 2,D = 1
3/10 = 0.3A