Functional Skills Level 2 — Statistics

The Mode

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The Most Frequent Value
Mode = the value that appears most often

Count how many times each value appears. The value with the highest count is the mode. A dataset can have no mode (all values appear once), one mode, or more than one mode (bimodal/multimodal).

Favourite Colour — Tally Chart Blue |||| | 6 Red |||| |||| 9 ★ MODE Red Green |||| 4 Yellow || 2 Pink ||| 3 Colour Tally Frequency Bar Chart — Tallest Bar = Mode 0 3 6 9 Blue Red ★ Green Yellow Pink

Example 1 — Mode of 3, 7, 3, 9, 5, 3, 7

Step 1
Count each value: 3 appears 3 times, 7 appears 2 times, 9 and 5 appear once each.
Step 2
Highest count = 3 times, for the value 3.
Step 3
Mode = \(\mathbf{3}\)

Example 2 — Bimodal data: 2, 4, 4, 6, 8, 8, 10

Step 1
Count: 4 appears twice, 8 appears twice, all others once.
Step 2
Two values tied for most frequent.
Step 3
Mode = \(\mathbf{4}\) and \(\mathbf{8}\) (bimodal)
No mode: If every value appears exactly once, the data has no mode. Don't write "0" — write "no mode".
✓ Quick Check 1 — Finding the mode
Question 1 of 10
Modal Class from a Frequency Table

In a frequency table the modal class is the row with the highest frequency. We say "class" because the data is often grouped or listed in a table rather than as raw numbers.

Shoe Size Frequency Table — Modal Class Shoe Size Frequency 6 5 7 11 8 18 ★ MODAL 9 14 10 8 Modal class = Size 8 (highest frequency: 18) Shoe Sizes — Modal Bar is Tallest Size 6 5 Size 7 11 Size 8 ★ 18 Size 9 14 Size 10 8

Example 3 — Modal class for number of pets

Pets: 0 (f=4), 1 (f=9), 2 (f=6), 3 (f=2)

Step 1
Find the highest frequency: 9 (for 1 pet)
Step 2
Modal class = 1 pet

Example 4 — Modal class for grouped data

Heights: 150–159 (f=3), 160–169 (f=11), 170–179 (f=14), 180–189 (f=7)

Step 1
Highest frequency = 14, in the class 170–179 cm
Step 2
Modal class = 170–179 cm
Modal class vs mode: For grouped data, report the class (e.g. 170–179 cm), not a single number.
✓ Quick Check 2 — Modal class from frequency tables
Question 1 of 10
When to Use the Mode — Categorical Data

The mode is the only average that works for categorical (non-numerical) data. You cannot calculate a mean or median for colours, names, or types.

Choosing the Right Average MEAN Numerical data No outliers Symmetrical spread e.g. heights of students MEDIAN Numerical data Outliers present Skewed data e.g. house prices, salaries MODE Any data type Categorical data Most popular item e.g. favourite colour, shoe size Transport to Work — Only the Mode Applies Car: 12 Walk: 8 Bus: 17 ★ Cycle: 5 Mode = Bus (most common). Cannot calculate mean or median of transport types.

Example 5 — Choosing the correct average

Step 1
Data: favourite fruit (apple, banana, apple, grape, apple, banana). Use the mode — categorical data.
Step 2
Mode = apple (appears 3 times)

Example 6 — When mode is misleading

Step 1
Exam scores: 10, 10, 50, 70, 85, 90. Mode = 10 (appears twice).
Step 2
10 is a poor representation of typical performance — only two students scored 10.
Step 3
Mean = \(\approx 52.5\), Median = 60 — both are more representative here.
Key rule: Mode = most popular. Use it for categorical data or when you need the most common item. For continuous numerical data, consider the mean or median instead.
✓ Quick Check 3 — When to use the mode
Question 1 of 10

Try It: Mode Summary

Check the key mode results across all three blocks.

#DataMode
13, 7, 3, 9, 5, 33
21, 2, 3, 4, 5No mode
34, 4, 6, 6, 84 and 6
4Freq table: size 6(f=5), size 7(f=12), size 8(f=9)Size 7
5red, blue, red, green, redred

Practice: Finding the Mode

Enter your answers as numbers.

#QuestionAnswerResult
1Find the mode of 3, 5, 5, 7, 9, 5, 2
2Find the mode of 8, 8, 8, 3, 3, 9, 1
3Find the mode of 21, 19, 21, 21, 25, 19
4Find the mode of 100, 105, 105, 105, 110, 120
5Find the mode of 6, 6, 9, 12, 12, 12, 15
6Find the mode of 4, 4, 7, 7, 7, 2
7Find the mode of 30, 40, 30, 50, 30, 60
8Find the mode of 2, 3, 4, 5
9Find the mode of 11, 13, 11, 15, 13, 11
10Find the mode of 90, 85, 90, 90, 70

⚠ Things to Watch Out For

  • Confusing mode with mean or median: The mode is simply the MOST FREQUENT value — no calculation needed. It does not involve adding or dividing.
  • Multiple modes: Data can have more than one mode (bimodal, trimodal). State ALL modes — don't just pick one.
  • No mode exists: If every value appears the same number of times, there is NO mode. Don't invent one.
  • Modal class in grouped data: The modal class is the group (class interval) with the HIGHEST FREQUENCY — not the group with the highest values or the highest midpoint.
  • Mode vs most appropriate average: The mode is best for categorical data (e.g. shoe size, colour) and is not affected by extreme values. For numerical data, mean or median may be more appropriate.
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