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Discrete Series & Tally Marks

4.5 Discrete Series & Tally Marks — Build frequency arrays using tally marks, understand frequency concepts, and calculate relative frequency distributions. CBSE Class 11 Statistics notes with interactive tally builder.

Notes

Discrete Series & Tally Marks

Class 11 Statistics — Frequency Arrays, Tally Construction, and Relative Frequency

Discrete Series — Definition

Discrete Series (Frequency Array)
A discrete series is a series where individual values differ from each other by a definite amount. Various values of the variable are shown along with their corresponding frequencies. For a discrete variable, the classification of its data is known as a ‘Frequency Array’.
A discrete variable takes a definite integral value and not fractional values. So, we have frequencies that correspond to each of its integral values.

Frequency

The number of times a given value appears in a distribution.

Frequency Array

A series that shows the frequency corresponding to discrete values of a variable. A discrete variable can only take on a finite or countable number of values, like number of children, shoe size, etc.

In a discrete series, the identity of various observations is not lost — it is possible to get back the original observations from the given frequency distribution.

Construction of Discrete Series using Tally Marks

Follow these 4 steps to construct a discrete series using the tally mark method.

Create a table with three column headings: (i) Variable (ii) Tally Marks (iii) Frequency.

Variable (Marks)Tally MarksFrequency
--
--
--
--
1 / 4

Relative Frequency Distribution

When actual frequencies are expressed as a percentage of total number of observations, relative frequencies are obtained.

Relative Frequency

$$\text{Relative Frequency} = \frac{f}{\Sigma f} \times 100$$
VariableFrequency (f)Relative Frequency (%)
1011.5%
2026.9%
3042.3%
4019.2%
Total (Sf)26100%

Try it yourself

Change the frequency values above — the relative frequencies update instantly in real time. Notice how the total always sums to 100%.

Key Takeaways

Key Takeaways

  • A discrete series (frequency array) shows each distinct value of a variable alongside how many times it occurs (its frequency).
  • Tally marks are a quick way to count frequencies: four vertical lines crossed by a diagonal for every fifth occurrence.
  • Four steps to construct: Prepare table ? List variable values ? Enter tally marks ? Count frequencies.
  • Relative frequency = (frequency / total observations) × 100, expressing each category as a percentage of the whole.
  • In a discrete series, individual observations can still be recovered from the frequency distribution.