Learning outcomes
- define a frequency table for numerical data
- organize raw numerical data into a compact table
- compute cumulative frequency in simple settings
- interpret the shape of a numerical summary
Why frequency tables are useful
- Raw numerical data can be long and hard to read.
- A frequency table summarizes how many times each value occurs.
2, 3, 2, 5, 4, 3, 2, 4, 5, 3
| Value | Frequency |
|---|---|
| 2 | 3 |
| 3 | 3 |
| 4 | 2 |
| 5 | 2 |
Parts of a numerical frequency table
- Value or class
- Frequency
- sometimes relative frequency
- sometimes cumulative frequency
Cumulative frequency
- Cumulative frequency is the running total of frequencies.
| Value | Frequency | Cumulative Frequency |
|---|---|---|
| 2 | 3 | 3 |
| 3 | 3 | 6 |
| 4 | 2 | 8 |
| 5 | 2 | 10 |
Ungrouped vs grouped tables
- Ungrouped frequency table: for individual values
- Grouped frequency table: for class intervals when there are many values
Interpretation questions
- Which value occurs most?
- What is the smallest value?
- What is the largest value?
- How many observations are at or below a value?
Exam hints and traps
- Frequency is count, not the value itself.
- Cumulative frequency must always increase or stay the same, never decrease.
- Total frequency must equal total number of observations.
- Do not confuse ordered raw data with cumulative frequency.
Quick practice
Data:1, 2, 2, 3, 4, 4, 4, 5
- Build the frequency table.
- Which value is most frequent?
- What is the cumulative frequency at
4?
Answer key
-
1 -> 12 -> 23 -> 14 -> 35 -> 1
47