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Continuous Series — Key Concepts

4.6 Continuous Series — Key Concepts — Learn class-interval terminology and the class-width formula for constructing grouped frequency distributions. CBSE Class 11 Statistics notes with interactive class-width calculator.

Notes

Continuous Series — Key Concepts

Class 11 Statistics — Class-Interval Terminology and Class-Width Formula

What is a Continuous Series?

Continuous Series (Grouped Frequency Distribution)
A continuous series is a series which represents continuous variables, showing a range of values of different items of the series. The measurements are only approximations and are expressed in class-intervals, i.e. within certain limits. Classes are framed without any break from beginning to end.
Continuous Series is also known as Frequency Distribution or Grouped Frequency Distribution or Series with Class-intervals or Series of Grouped Data.

Real-life analogy: School attendance

Imagine your school has 1,000 students. Instead of listing all 1,000 ages individually, you group them: 10–12 years (300 students), 12–14 (400), 14–16 (200), 16–18 (100). That’s a continuous series — you’ve grouped the data into class-intervals without gaps.

Important Terms

Click each term to see its full explanation and example.

Class

A group of numbers in which items are placed, such as 0–10, 10–20, 20–30, etc. Must be clearly defined, exhaustive (every value falls into some class), and mutually exclusive (each value belongs to only one class).

Example:

In the distribution 0–10, 10–20, 20–30 — each range is one class.

Class Limits

l1 = Lower limit, l2 = Upper limit

The lowest and highest values of the variables within a class. Lower limit (l1): the lowest value of a class. Upper limit (l2): the highest value of a class.

Example:

In the class 10–20, l1 = 10 and l2 = 20.

Class-Interval

i = l2 - l1

The difference between the lower limit (l1) and upper limit (l2) of a class. Indicated by i or c. Also known as magnitude, size, or length of the class.

Example:

In class 10–20, class-interval = 20 - 10 = 10.

Range

Range = Largest - Smallest

Difference between the lower limit of the first class-interval and the upper limit of the last class-interval.

Example:

Classes 0–10 to 70–80 ? Range = 80 - 0 = 80.

Mid-Point

(l1 + l2) / 2

The central point of a class-interval.

Example:

Mid-point of 10–20 = (10 + 20) / 2 = 15.

Frequency

Sf = N

Number of times a given value appears. Class frequency (f) = number of observations in a class. Sum of frequencies = Sf or N. Frequency distribution = table showing how values distribute across classes.

Example:

If 5 students scored 10–20 marks, frequency of that class = 5.

Class-Width Formula

The width of each class in a continuous series is determined by this formula:

Class Width

$$\text{Width of Class} = \frac{\text{Largest Observation} - \text{Smallest Observation}}{\text{Number of Classes Desired}}$$
Round up to the nearest convenient integer. As far as possible, all classes should be of equal width. A frequency distribution with equal class width is convenient to represent on a diagram and easy to analyse.

Class-Width Calculator

80

10

7

Class Width =

10

(80 - 10) / 7 = 10 ? rounded up to 10

Resulting Classes:

10–20
20–30
30–40
40–50
50–60
60–70
70–80

Key Takeaways

Key Takeaways

  • A continuous series (grouped frequency distribution) arranges continuous variables into class-intervals without gaps.
  • Key terms: Class, Class Limits (lower & upper), Class-Interval (width), Range, Mid-Point, and Frequency.
  • Class Width = (Largest Observation - Smallest Observation) / Number of Classes Desired — always round up.
  • All classes should ideally have equal width for easy analysis and diagrammatic representation.
  • The mid-point of a class = (Lower Limit + Upper Limit) / 2, used as the representative value for that class.