Statistics · Ch 3 — Measures of Central Tendency
Meaning, Objectives and Types of Series
Meaning, Objectives and Types of Series
Raw data — a long list of marks, wages, ages or sales figures — is hard to grasp at a glance. A measure of central tendency condenses an entire distribution into ONE single, representative value around which most of the observations tend to cluster. This chapter, a core computational unit of the Gujarat Std 11 Commerce Statistics (GSHSEB) syllabus, builds five such measures — arithmetic mean, median, mode, geometric mean and harmonic mean — and shows exactly how to compute each, whichever form the data arrives in.
Objectives of studying central tendency:
- To get one single value that describes the characteristic of the entire data set.
- To facilitate comparison between two or more distributions (e.g. average marks of two sections).
- To provide a base for further statistical analysis — dispersion, skewness and correlation (covered in later chapters) are all measured AROUND a central value.
- To help in decision-making and planning, since a summarised figure is far more usable than raw data.
Types of statistical series — the SAME formula is never applied blindly; the shape of the data decides the working method:
| Series type | What it looks like | Example |
|---|---|---|
| Individual series (raw/ungrouped data) | Every observation listed separately, no repetition grouped | Marks of 5 students: 45, 60, 55, 70, 50 |
| Discrete series (ungrouped frequency distribution) | Distinct values, each with its own frequency | Number of children per family: = 0,1,2,3 with frequency |
| Continuous series (grouped frequency distribution) | Data grouped into class intervals, each with a frequency | Marks grouped as 0–10, 10–20, 20–30, … with frequency |
Every measure of central tendency in this chapter is computed three ways — once for each series type — because the working method (though built on the same underlying idea) genuinely differs by series type. A student preparing for the Gujarat Board Std 11 Commerce Statistics exam must be equally comfortable with all three.
The tendency of numerical data to cluster around some central value; a measure of central tendency is a single figure representing the whole distribution.
Raw, ungrouped data in which every observation is listed separately without any repetition being grouped into a frequency.
A frequency distribution of distinct, separately countable values, each shown against its own frequency.
A frequency distribution in which data is grouped into class intervals (e.g. 0–10, 10–20), each interval carrying a frequency.