lesson
An average needs a clearly defined group
1 · Learn
Aggregation summarises records using counts, sums or averages. Define which rows are included and how missing values are handled. An average of group averages is not generally the overall average unless group sizes are equal or appropriately weighted.
Keep the denominator visible. Counting visits, people and completed tasks answers different questions even if the numbers happen to match.
2 · Worked example
Group A has two scores averaging 10; B has eight averaging 20. Overall mean is (2×10 + 8×20)/10 = 18, not 15.
3 · Your turn
Why is averaging 10 and 20 directly wrong for those unequal groups?
Check your answer
It gives each group equal weight despite different numbers of scores.
4 · Apply your learning
Build an invented summary table that labels both the measure and number of records used.
Adult guidance and safety
Work in an approved local sandbox with invented records and test accounts. Do not access other people's systems or collect real credentials. Practical project evidence is required in addition to these explanations; this is not a specified GCSE Computer Science course.
Open your writing and drawing pad
Write, draw or show your working. Use a mouse, pen or finger. This pad is not a submitted answer.
Not saved to your account. Download your drawing as PNG and your typed notes as TXT before leaving or refreshing. They are separate files. Do not enter private information.
Open a picture saved on this device to draw on it again. Opening replaces the drawing, but Undo can restore it. PNG only, up to 4 MB and 4096 × 4096 pixels. The picture stays in this browser; it is not uploaded. Paper lines in a saved picture become part of that picture.
Clear the drawing? Your typed notes will stay. You can undo this action.
Your pad is empty.
Open a UTF-8 TXT file from this device, up to 40 KB and 10,000 characters. It stays in this browser. Opening can be undone until you type again. Downloads keep a new copy; they do not change the file you opened.
Replace the notes on this page with the opened file? Download the current notes first if you want to keep them.
Typed notes are not submitted answers.
Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
Practice this lesson
Lesson resources
Browse the available practice activities and worksheets for this lesson.
Your progress