Mode of Grouped Data Class 10: Formula & Examples

Quick answer: The mode of grouped data is the value that occurs most often, and it is found with

Mode = l + ((f₁ − f₀) / (2f₁ − f₀ − f₂)) × h

where l = lower limit of the modal class, f₁ = frequency of the modal class, f₀ = frequency of the class before it, f₂ = frequency of the class after it, and h = class size.

Unlike ungrouped data — where you just pick the most repeated value — grouped data hides individual values inside intervals. So you can’t read the mode off directly. Instead you first find the modal class (the interval with the highest frequency), then use the formula to pin down a value inside that class.

In this guide we identify the modal class, define every symbol, and work a full example that gives Mode = 24.17, using the same data set as the mean and median guides so you can compare all three.

What is the mode, and what is the modal class?

The mode is the observation with the maximum frequency — the value that appears most often. For ungrouped data it’s obvious: in 2, 6, 4, 5, 0, 2, 1, 3, 2, 3, the number 2 appears three times, so the mode is 2.

For grouped data you can only locate a class with the maximum frequency, called the modal class. The mode is then a specific value inside that class, calculated with the formula. (We restrict ourselves to data with a single mode; data with two or more equal maximum frequencies is called multimodal and is out of scope here.)

Our data set (shared across the Statistics guides):

The highest frequency is 15, so the modal class is 20–30.

The mode formula, with every variable defined

Mode = l + ((f₁ − f₀) / (2f₁ − f₀ − f₂)) × h

• Meaning in words: start at the lower limit of the modal class, then move into it by an amount that depends on how much taller the modal class is than its neighbours.
• Variables:
  • l = lower limit of the modal class
  • f₁ = frequency of the modal class
  • f₀ = frequency of the class preceding the modal class
  • f₂ = frequency of the class succeeding the modal class
  • h = size of the class interval
• Condition: class intervals must be continuous and (for this formula) of equal size.

Worked example — finding the mode step by step

Step 1 — Identify the modal class. The maximum frequency is 15, so the modal class is 20–30.

Step 2 — Read off the values.

• l = 20 (lower limit of 20–30)
• f₁ = 15 (modal class frequency)
• f₀ = 10 (frequency of 10–20, the class before)
• f₂ = 8 (frequency of 30–40, the class after)
• h = 10 (class size)

Step 3 — Substitute and simplify.

Mode = 20 + ((15 − 10) / (2×15 − 10 − 8)) × 10 = 20 + (5 / (30 − 18)) × 10 = 20 + (5 / 12) × 10 = 20 + 4.17 = 24.17

So the mode of this data is 24.17 — the value that best represents the “most common” region of the distribution.

examfront’s Topic Practice throws you distributions where the modal class isn’t the obvious middle one — the fastest way to stop mis-reading f₀ and f₂.

🎬 Quick challenge: Can you spot the modal class from the frequency table? 📊

A second quick example (smaller numbers)

Suppose family sizes are grouped as 1–3, 3–5, 5–7, 7–9 with frequencies 5, 9, 12, 4. The maximum frequency is 12, so the modal class is 5–7.

• l = 5, f₁ = 12, f₀ = 9, f₂ = 4, h = 2

Mode = 5 + ((12 − 9) / (2×12 − 9 − 4)) × 2 = 5 + (3 / 11) × 2 = 5 + 0.55 = 5.55.

So the most common family size is about 5.55 members — read as “between 5 and 6, closer to 5 or 6 depending on the neighbours.”

examfront’s Chapter Quizzes pair mode questions with mean and median ones, so you practise choosing the right formula, not just plugging into a known one.

Mode vs. mean vs. median — when to use the mode

The mode answers a different question from the mean and median. Use the mode when you need the most frequent or most popular value, such as:

• the most common shoe size a shop sells,
• the most-watched TV programme,
• the consumer item in greatest demand,
• the colour of car most people own.

For our shared data, mode = 24.17, while the mean is 25.8 and the median is 25.33. All three describe the “centre,” but each in its own way — which is exactly why Class 10 teaches all three.

examfront’s Mistake Identification catches the classic mode slip — swapping f₀ and f₂ — the moment it happens, so it doesn’t become a habit.

🎬 Quick challenge: Can you calculate the mode using the grouped-data formula? 📊

Key Takeaways

• Mode of grouped data: Mode = l + ((f₁ − f₀)/(2f₁ − f₀ − f₂)) × h.
• The modal class is the interval with the highest frequency — find it first.
• f₀ is the frequency before the modal class and f₂ is the frequency after it — don’t swap them.
• Class intervals must be continuous and equal in size before applying the formula.
• Use the mode when the “most frequent / most popular” value is what you need.

Quick Facts

• Formula: Mode = l + ((f₁ − f₀)/(2f₁ − f₀ − f₂)) × h.
• Modal class = class with the maximum frequency.
• For our data, modal class = 20–30, mode = 24.17.
• The mode can be less than, equal to, or more than the mean.
• Data with two or more equal top frequencies is called multimodal (out of Class 10 scope).

Common Mistakes

1. Picking the class with the highest class mark instead of the highest frequency — the modal class is about frequency, not the size of the interval.
2. Swapping f₀ and f₂ — f₀ is the class before the modal class, f₂ the class after.
3. Forgetting to make classes continuous — convert 1–3, 4–6 style classes to continuous form first.
4. Miscomputing the denominator — it is 2f₁ − f₀ − f₂, a common spot for sign slips.
5. Confusing mode with mean — mode = most frequent value, mean = average; they are usually different numbers.

FAQ

What is the formula for the mode of grouped data in Class 10? Mode = l + ((f₁ − f₀) / (2f₁ − f₀ − f₂)) × h, where l is the lower limit of the modal class, f₁ its frequency, f₀ the frequency of the class before it, f₂ the frequency of the class after it, and h the class size.

What is the modal class? The modal class is the class interval with the highest frequency. You locate it first, then apply the mode formula to find a value inside it.

How do you find the mode of grouped data step by step? Identify the modal class (maximum frequency), read off l, f₁, f₀, f₂ and h, then substitute into Mode = l + ((f₁ − f₀)/(2f₁ − f₀ − f₂)) × h and simplify.

What is the difference between mode and mean? The mode is the most frequent value (best for the most popular item); the mean is the arithmetic average of all values (affected by extremes). For our data, mode = 24.17 and mean = 25.8.

When is the mode the best measure of central tendency? When you need the most frequent or most popular value — such as the most common shoe size, most-watched programme, or item in greatest demand.

Related Concepts

• Measures of central tendency — how the mode sits alongside mean and median.
• Mean of grouped data — the average and its three methods.
• Median of grouped data — the middle value and cumulative frequency.
• Frequency distribution (Class 9) — reading frequencies from a grouped table.

Want to nail every modal-class trap? Practise mixed questions on examfront and use Strength & Weakness Analysis to see whether it’s the modal class or the formula that’s costing you marks.