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Frequency Distribution Class Formation Class 11 Economics

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EconomicsCBSE Class 11 · Organisation of Data

Frequency Distribution: Building Classes, Class Marks and Cumulative Frequency

Updated 17 October 2026 · Fact-checked

A frequency distribution shows classes of a variable with the number of observations in each. Class width is about range divided by number of classes. In the exclusive method the upper limit is excluded; in the inclusive method both limits are included, and are converted to exclusive form by subtracting half the gap from lower limits and adding it to upper limits. Class mark = (lower + upper) / 2.

The gap between 19 and 20 is 1, so half of it (0.5) is subtracted from lower limits and added to upper limits; then mark = (L + U) ÷ 2.

Illustration drawn for QuestionBuddy.

Understand Frequency Distribution and Class Formation

Frequency distribution. A table showing the classes of a variable with the frequency (number of items) in each. Steps: (1) find the range = largest − smallest value; (2) decide the number of classes (usually 5 to 15); (3) fix class width ≈ range ÷ number of classes (rounded to a convenient value); (4) set class limits; (5) tally and count.

Terms. Class limits: lower and upper. Class interval (width) = upper limit − lower limit. Class mark (mid-point) = (lower limit + upper limit) ÷ 2. Frequency: number of observations in the class.

Exclusive method. Classes such as 0-10, 10-20, 20-30: the upper limit of a class is the lower limit of the next; an item equal to 10 goes to 10-20 (the upper limit is excluded). Suitable for continuous variables.

Inclusive method. Classes such as 10-19, 20-29: both limits are included. For a continuous variable it must be converted to exclusive by an adjustment factor = (lower limit of next class − upper limit of this class) ÷ 2; subtract it from every lower limit and add it to every upper limit. For 10-19, 20-29: adjustment = (20 − 19)/2 = 0.5, giving 9.5-19.5, 19.5-29.5.

Tally marks. Bundles of five (four vertical strokes crossed by a fifth) are used to count frequencies without error.

Cumulative frequency. Running total of frequencies: less than (adds from the first class) and more than (from the last class). Relative frequency = frequency ÷ total.

Loss of information. Grouping hides individual values; we know only that 4 students scored in 10-20, not exactly what.

Worked data (20 marks). 12, 35, 27, 41, 18, 29, 33, 45, 22, 38, 9, 31, 26, 48, 15, 37, 24, 43, 19, 20. Range = 48 − 9 = 39. Classes of width 10 from 0 to 50 (exclusive): frequencies 1, 4, 6, 5, 4 (total 20); cumulative frequency 1, 5, 11, 16, 20.

Table: class, tally, frequency, cumulative frequency, class mark.

Frequency Distribution and Class Formation: key facts

Class width
About Range / number of classes
Range = largest - smallest
Class mark
(Lower + upper) / 2
Mid-point
Adjustment
(Lower of next class - upper of this class) / 2
Inclusive to exclusive
Cumulative frequency
Running total of frequencies
Less than / more than

How to answer Frequency Distribution and Class Formation questions

Questions give raw data or classes and ask for a table, class marks or conversion.

  1. 1Find the range and choose a convenient width.
  2. 2Write exclusive classes and count with tally marks.
  3. 3Check that frequencies add to the total.
  4. 4For inclusive classes compute the adjustment factor.
  5. 5Compute class marks and cumulative frequencies from the final classes.

Frequency Distribution and Class Formation in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Test marks of 20 students

Suppose 20 students' marks in a test (out of 50) are recorded and the teacher wants a table with classes of width 10.

Build the frequency distribution and say how many scored below 30.

Try it first, then show the solutionSolution
  1. Using classes 0-10 to 40-50 with exclusive limits, count the marks.
  2. Frequencies are 1, 4, 6, 5, 4 (total 20).
  3. Cumulative up to 30: 1 + 4 + 6 = 11 students scored below 30.

Answer: 11 students scored below 30.

Memory hook: Add the first three.

Tricks to remember Frequency Distribution and Class Formation

Short memory aids. Say each one aloud once, then use it on a question the same day.

  • Exclusive: top excluded

    In exclusive classes, the upper limit belongs to the next class.

    Use it when: Method

  • Half the gap

    Adjustment is half the gap between classes.

    Use it when: Conversion

  • Mid is mean of limits

    Class mark = (L + U)/2.

    Use it when: Class mark

Frequency Distribution and Class Formation: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Class mark · 2 marks · Very short answerBoard level

Find the class mark of the class 20-30, and the width.

Try it first, then show the solutionSolution
  1. Class mark = (20 + 30)/2 = 25 (1 mark).
  2. Width = 30 - 20 = 10 (1 mark).

Answer: Class mark 25; width 10.

Example 2: Inclusive to exclusive · 3 marks · Short answerBoard level

Convert the classes 10-19, 20-29, 30-39, 40-49 into exclusive form and give the adjustment factor.

Try it first, then show the solutionSolution
  1. Adjustment = (20 - 19) / 2 = 0.5 (1 mark).
  2. Subtract 0.5 from lower limits and add 0.5 to upper limits (1 mark).
  3. Classes: 9.5-19.5, 19.5-29.5, 29.5-39.5, 39.5-49.5 (1 mark).

Answer: Adjustment 0.5; 9.5-19.5 and so on.

Example 3: Build the table · 5 marks · Long answerHarder board level

Raw marks of 20 students: 12, 35, 27, 41, 18, 29, 33, 45, 22, 38, 9, 31, 26, 48, 15, 37, 24, 43, 19, 20. Prepare a frequency distribution with exclusive classes of width 10 starting at 0 and find the cumulative frequencies.

Try it first, then show the solutionSolution
  1. Range = 48 - 9 = 39, width 10 gives 5 classes (1 mark).
  2. Frequencies for 0-10, 10-20, 20-30, 30-40, 40-50 are 1, 4, 6, 5, 4 by tally (1 mark).
  3. Check total: 1 + 4 + 6 + 5 + 4 = 20 (1 mark).
  4. Cumulative frequencies: 1, 5, 11, 16, 20 (1 mark).
  5. Class marks: 5, 15, 25, 35, 45 (1 mark).

Answer: Frequencies 1,4,6,5,4; cumulative 1,5,11,16,20.

Example 4: Reading the table · 3 marks · Short answerHarder board level

From the table above find (a) how many scored 30 or more (b) the percentage in the class 20-30 (c) the class in which a mark of exactly 30 falls.

Try it first, then show the solutionSolution
  1. 30 or more: 5 + 4 = 9 (equivalently 20 - 11 = 9) (1 mark).
  2. Percentage in 20-30 = 6 / 20 x 100 = 30 per cent (1 mark).
  3. Mark 30 falls in 30-40, as the exclusive method excludes the upper limit of 20-30 (1 mark).

Answer: 9 students; 30 per cent; class 30-40.

Example 5: Choosing class width · 5 marks · Long answerHOTS / competency

A researcher groups the same 20 marks into inclusive classes 10-19, 20-29, 30-39, 40-49 and cannot place the mark 9. Explain the problem, find the frequencies of the four classes, and suggest a remedy.

Try it first, then show the solutionSolution
  1. Mark 9 is below the first class limit, so the classes do not cover the data (1 mark).
  2. Frequencies of the four classes are 4, 6, 5, 4, adding to 19, not 20 (1 mark).
  3. One observation is lost (1 mark).
  4. Remedy: begin the first class at 0 or 5 (e.g. 0-9) so all values are covered (1 mark).
  5. Check that the total equals the number of observations (1 mark).

Answer: Frequencies 4,6,5,4 miss the mark 9; start classes lower.

Where students lose marks in Frequency Distribution and Class Formation

The slips examiners see most often, and what to write instead.

  • Mistake: Adding the gap

    Adjustment direction.

    Wrong working

    Add 0.5 to lower limits.

    Right working

    Subtract from lower, add to upper.

    Do this: Lower down, upper up.

    Usually costs: 1 mark.

  • Mistake: Class mark with upper only

    Formula slip.

    Wrong working

    Class mark = upper limit / 2.

    Right working

    (Lower + upper) / 2.

    Do this: Mid-point.

    Usually costs: 1 mark.

  • Mistake: Frequencies not adding

    Skipped check.

    Wrong working

    Totals 19 for 20 items.

    Right working

    Always check the total.

    Do this: Count.

    Usually costs: 1 mark.

Exam tips

  • Always write range, width and number of classes.
  • Check the sum of frequencies.
  • Convert inclusive to exclusive for continuous data.
  • Compute cumulative frequency from the final table.

Practice questions on Frequency Distribution and Class Formation

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

  1. Q1 · 1 mark · MCQBoard level

    In the classes 0-5, 5-10 and 10-15 (exclusive method), an observation of exactly 10 is counted in
    (a) 5-10 (b) 10-15 (c) both (d) neither

    Hint

    Upper limit excluded.

    Answer

    (b).

  2. Q2 · 1 mark · Assertion-reasonHarder board level

    Assertion (A): Grouped data lose some information.
    Reason (R): Individual observations cannot be recovered from a frequency table.
    (a) Both A and R are true and R is the correct explanation of A.
    (b) Both A and R are true but R is not the correct explanation of A.
    (c) A is true but R is false.
    (d) A is false but R is true.

    Hint

    Summary cost.

    Answer

    (a).

  3. Q3 · 2 marks · Very short answerHarder board level

    Find the class marks of the classes 0-10, 10-20 and 20-30, and the relative frequency of the class 20-30 if its frequency is 6 out of 20.

    Hint

    Mid-points.

    Answer

    Class marks 5, 15, 25. Relative frequency = 6 / 20 = 0.30 (30 per cent).

  4. Q4 · 4 marks · Case-basedHarder board level

    Read and answer.
    Suppose the cumulative (less than) frequencies are 1, 5, 11, 16 and 20 for upper limits 10, 20, 30, 40, 50.
    (a) Find the frequency of each class. (2)
    (b) How many are below 40? (1)
    (c) How many are 40 or more? (1)

    Hint

    Differences.

    Answer

    (a) 1, 4, 6, 5, 4. (b) 16. (c) 20 - 16 = 4.

  5. Q5 · 3 marks · Short answerHOTS / competency

    Suppose incomes of 25 families are grouped into classes with width 1,000 from 0 to 5,000. Explain how changing the width to 500 changes the table and what is gained and lost.

    Hint

    Width trade-off.

    Answer

    The number of classes doubles from 5 to 10, giving more detail but a longer table with fewer observations in each class. A wider class gives a shorter, clearer table but loses detail.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

  1. 1.Class mark?Show answer

    (L + U)/2.

  2. 2.Adjustment factor?Show answer

    Half the gap between classes.

  3. 3.Exclusive method?Show answer

    Upper limit excluded.

  4. 4.Cumulative frequency?Show answer

    Running total.

  5. 5.Tally bundle?Show answer

    Five.

  6. 6.Relative frequency?Show answer

    Frequency / total.

Frequency Distribution and Class Formation: frequently asked questions

What is a frequency distribution?

A table of classes and their frequencies.

What is class width?

Upper limit minus lower limit.

When to use exclusive?

For continuous variables.

What is a tally mark?

A counting stroke grouped in fives.

What is lost in grouping?

Individual values.