Statistics — Study Notes for TS TET

Overview

Statistics is a fundamental topic in the TS TET Mathematics section, appearing in both Paper I (Classes 1-5) and Paper II (Classes 6-8). At the primary and upper primary levels, statistics focuses on organising, representing and interpreting data using simple measures of central tendency (mean, median, mode) and spread (range).

This topic carries direct questions in the content section and also appears in pedagogy questions where you must suggest appropriate methods for teaching data handling. Examiners frequently test your ability to calculate averages from grouped/ungrouped data and interpret bar graphs, pictographs and pie charts. Mastery here requires both computational accuracy and conceptual clarity about when to use which measure.

For TET purposes, focus on quick mental calculation techniques, understanding the behaviour of mean/median/mode when data changes, and recognising common student misconceptions about averages.

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Key Concepts

• **Data** is a collection of facts, figures or observations. It can be **primary** (collected first-hand) or **secondary** (obtained from existing sources).

• **Mean (Arithmetic Average)** is the sum of all observations divided by the number of observations. It uses every data point and is sensitive to extreme values (outliers).

• **Median** is the middle value when data is arranged in ascending or descending order. For an even number of observations, it is the average of the two middle values. Median is resistant to outliers.

• **Mode** is the value that occurs most frequently. A data set can have no mode, one mode (unimodal), or multiple modes (bimodal/multimodal).

• **Range** measures spread: Range = Highest value − Lowest value. It indicates how scattered the data is but is affected by extreme values.

• **Frequency** is the number of times a particular observation occurs. A **frequency distribution table** organises data by grouping observations with their frequencies.

• **Data Representation** includes pictographs, bar graphs, double bar graphs, pie charts and line graphs. Each serves different purposes depending on the nature of data.

• The **appropriate measure** depends on context: mean for symmetric data without outliers, median for skewed data or when outliers exist, mode for categorical data or finding the most common item.

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Formulas / Key Facts

| Measure | Formula / Rule | |---------|----------------| | Mean (Ungrouped) | Mean = (Sum of all observations) ÷ (Number of observations) | | Mean (Grouped) | Mean = Σ(f × x) ÷ Σf, where f = frequency, x = class mark | | Class Mark | Class Mark = (Lower limit + Upper limit) ÷ 2 | | Median (Odd n) | Middle value = value at position (n + 1) ÷ 2 | | Median (Even n) | Average of values at positions n ÷ 2 and (n ÷ 2) + 1 | | Mode | Value with highest frequency | | Range | Highest observation − Lowest observation |