A frequency table lists each possible value in a dataset alongside how many times it occurred — its frequency. Adding up the frequency column gives the total number of data values, which you need before calculating an average such as the mean, median or mode from the table.
Example 1 — Reading the table
Step 1
The table shows 20 matches were played (\(\sum f = 20\)).
Step 2
The most common number of goals was 2 (frequency 7) — this is the mode.
Step 3
In 2 matches, 0 goals were scored; in 7 matches, 2 goals were scored.
Tip: Always check \(\sum f\) equals the total number of observations before calculating any averages.
✓ Quick Check 1 — Reading frequency tables
Question 1 of 10
Mean from a Frequency Table — the fx Column
\[\text{Mean} = \frac{\sum fx}{\sum f}\]
Add an fx column (value × frequency). Sum it to get \(\sum fx\), then divide by \(\sum f\).
Example 2 — Number of siblings: 0(f=4), 1(f=8), 2(f=5), 3(f=3)
⚠ Common mistake: Dividing by the number of rows instead of \(\sum f\). Always use the total frequency column sum.
✓ Quick Check 2 — Mean from frequency tables
Question 1 of 10
Median and Mode from a Frequency Table
Use a cumulative frequency column to locate the median. The mode is simply the value with the highest frequency.
Example 3 — Finding the median using cumulative frequency
Step 1
Build cumulative frequency: running total of frequencies going down the table.
Step 2
\(n = 20\): median positions are 10th and 11th values.
Step 3
Cumulative frequency reaches 7 after x=1, and 14 after x=2. Both positions 10 and 11 fall in x=2.
Step 4
Median = \(\mathbf{2}\) goals.
As in Lesson 18.3 — Mode, the mode is just the x-value with the highest frequency — in the table above, x=2 has frequency 7 (the highest), so the mode is 2 goals.
Tip: For even \(n\): median position = between \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th. Find which row both positions fall in using cumulative frequency.
✓ Quick Check 3 — Median, mode, and cumulative frequency
Question 1 of 10
Try It: Frequency Table Summary
Table — Pets per household: 0(f=3), 1(f=6), 2(f=4), 3(f=2). Use this to answer the questions below.
#
Question
Answer
1
What is Σf?
15
2
What is Σfx?
0+6+8+6 = 20
3
What is the mean?
20 ÷ 15 ≈ 1.33
4
What is the mode?
1 pet (f=6)
5
What is the median? (n=15, position 8)
1 pet (cum.f reaches 9 at x=1)
Practice: Averages from Frequency Tables
Enter your answers as numbers.
#
Question
Answer
Result
1
Table: 2 (f=3), 3 (f=5), 4 (f=2). Find the mean.
2
Table: 1 (f=2), 2 (f=3), 3 (f=5). Find the mean.
3
Table: 5 (f=2), 6 (f=8), 7 (f=3). What is the modal value?
4
Table: 10 (f=4), 11 (f=7), 12 (f=9). What is the total frequency?
Table: 8 (f=6), 9 (f=3), 10 (f=1). What is the modal value?
8
Table: 2 (f=5), 3 (f=5). What is the total frequency?
9
Table: 1 (f=1), 2 (f=2), 3 (f=7). Find the mean.
10
Table: 20 (f=2), 21 (f=3), 22 (f=5). What is the modal value?
⚠ Things to Watch Out For
Dividing by number of rows instead of total frequency: Mean = Σfx ÷ Σf (total of all frequencies, not number of rows in the table).
Not creating the fx column: You must multiply each value by its frequency (fx) before summing. Adding up the values column directly ignores how many times each occurs.
Finding median — not using cumulative frequency: Build a cumulative frequency column to identify which group the median falls in. Don't guess from the frequencies alone.
Modal class vs modal value: From a frequency table, the mode is the value (or class) with the highest frequency — not the largest value or the middle row.
Σf ≠ number of rows: The total frequency Σf is the sum of all the frequency values. Always add the frequency column, not count the rows.