MPESB Group · Bite-size lessons
Statistics
About 6 min · Mathematics · English
Time worked out from the lesson's 326 words at 150 words a minute, plus a minute for each question.
The examiners focus on three central measures of central tendency—mean, median, and mode—along with their calculation from raw data and frequency distributions.
Key ideas
- 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 the best measure when data has outliers or is skewed.
- Mode is the value that occurs most frequently. A dataset can have no mode, one mode (unimodal), or multiple modes (bimodal/multimodal).
- Frequency Distribution organizes data into classes with their frequencies, making calculation of mean/median/mode systematic for large datasets.
- Class Mark (Mid-value) = (Lower limit + Upper limit) / 2. This represents each class in grouped data calculations.
Watch out for
- Forgetting to arrange data before finding median → Always sort data in ascending order first. Random order gives wrong middle value.
- Confusing cumulative frequency with frequency → cf is running total used to locate median class; f is the frequency of that specific class used in formula.
- Using wrong class limits in median/mode formula → Always use the lower limit (L) of the median/modal class, not upper limit or class mark.
Quick reference
- Mean = Σfx / Σf (uses all values; affected by outliers)
- Median position: (n+1)/2 for odd; average of middle two for even
- Mode = highest frequency value; use formula for grouped data
- Median class: where cumulative frequency first crosses n/2
- Empirical relation: Mode = 3 × Median − 2 × Mean
Check yourself: 3 questions
1. The mean of 5 numbers is 20. If one number 16 is removed, what is the mean of the remaining 4 numbers?
2. Find the median of the following data: 15, 22, 18, 30, 25, 20, 28
3. The marks obtained by 10 students are: 35, 42, 35, 50, 35, 48, 42, 35, 50, 45. What is the mode of this data?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 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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