AP TET · Bite-size lessons

Statistics

About 6 min · Mathematics and Science (Paper II) · English

Time worked out from the lesson's 390 words at 150 words a minute, plus a minute for each question.

Statistics is the branch of mathematics that deals with collecting, organising, analysing and interpreting numerical data. For AP TET Paper II, this topic connects mathematical skills with real-world applications—a key pedagogical objective for classes 6–8.

Key ideas

• Data is a collection of facts or numbers gathered for analysis. Data 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. It is unaffected by outliers and better represents "typical" value in skewed distributions.
• Mode is the observation that occurs most frequently. A data set can be unimodal (one mode), bimodal (two modes), multimodal or have no mode if all values appear equally.
• Range measures spread: Range = Highest value − Lowest value. A larger range indicates greater variability.

Watch out for

• Forgetting to arrange data before finding median. Wrong: Picking the middle position from unordered data. Fix: Always sort data in ascending or descending order first.
• Confusing mean formula for grouped vs ungrouped data. Wrong: Adding frequencies directly instead of computing Σ(f × x). Fix: For frequency data, multiply each observation by its frequency, sum these products, then divide by total frequency.
• Assuming every data set has exactly one mode. Wrong: Forcing a single mode answer when two values share the highest frequency. Fix: Recognise bimodal or "no mode" situations and state them clearly.

Quick reference

• Mean = Total sum ÷ Count — sensitive to outliers.
• Median = Middle value (arrange first!) — robust to outliers.
• Mode = Most frequent value — useful for categorical data.
• Range = Max − Min — simple measure of spread.
• For odd n: Median at (n + 1)/2; for even n: average of two middle terms.

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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