Statistics and Data Handling

Overview

Statistics and Data Handling forms a crucial component of the upper-primary mathematics curriculum and appears consistently in WB TET Paper II. This topic tests your ability to organise raw data, calculate measures of central tendency (mean, median, mode), and interpret graphical representations such as bar graphs, histograms, pie charts and frequency polygons.

For the TET examination, you must demonstrate both computational proficiency and pedagogical understanding. Questions typically involve calculating averages from grouped or ungrouped data, identifying the correct graph type for given data, and interpreting visual representations. Since this topic connects mathematics with real-world applications—census data, weather patterns, classroom attendance—it is ideal for activity-based teaching, making it a favourite area for pedagogy-linked questions.

Mastery here requires understanding when to use each measure of central tendency, recognising their limitations, and knowing how to represent data visually for maximum clarity.

Key Concepts

• **Data** refers to facts or figures collected for analysis. It can be primary (collected firsthand) or secondary (obtained from existing sources).

• **Raw data** is unorganised information; when arranged systematically using tally marks or frequency tables, it becomes **organised data**.

• **Frequency** is the number of times a particular observation occurs in a dataset.

• **Mean (Arithmetic Average)** is the sum of all observations divided by the total number of observations—best used when data has no extreme outliers.

• **Median** is the middle value when data is arranged in ascending or descending order—preferred when data contains extreme values.

• **Mode** is the most frequently occurring observation—useful for categorical data like favourite colours or shoe sizes.

• **Range** is the difference between the highest and lowest values, indicating the spread of data.

• **Class interval** is a group of values in grouped data (e.g., 10–20, 20–30), with **class mark** being the midpoint of each interval.

Formulas / Key Facts

**Mean (Ungrouped Data)** Mean = Sum of all observations ÷ Number of observations Mean = Σx ÷ n

**Mean (Grouped Data — Direct Method)** Mean = Σ(f × x) ÷ Σf where f = frequency, x = class mark (midpoint of class interval)

**Median (Ungrouped Data)**

• Arrange data in ascending order
• If n is odd: Median = value at position (n + 1) ÷ 2