IP EMaths Notes (Upper Sec, Year 3-4): 15) Statistics and Data Handling

Study guide08 Nov 2025, 00:00 ZUpdated 30 Nov 2025

Summarise data with mean, median, mode, and cumulative frequency, and interpret scatter plots with correlation language.

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Q: What does IP EMaths Notes (Upper Sec, Year 3-4): 15) Statistics and Data Handling cover?
A: Summarise data with mean, median, mode, and cumulative frequency, and interpret scatter plots with correlation language.

The core idea is simple: Organise the data first; the calculation is easier after the table is clean.

Use it as a working check: Use mean, median, mode, range, IQR, and standard deviation to describe different parts of a dataset. For scatter plots, say correlation, not cause.

Then go one layer deeper: Work through the grouped-table examples to practise cumulative frequency, percentiles, and clear interpretation sentences that compare centre, spread, and pattern.

Statistics questions reward tidy tables and well-labelled graphs. Document your calculator steps so you can replicate them under exam conditions.

Keep the full topic roadmap handy via our IP Maths tuition hub so you can jump into related drills, quizzes, or diagnostics as you move through these notes.

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These notes align with SEAB GCE O-Level Mathematics (4052) content used in IP programmes (exams from 2026).

Status: SEAB O-Level Mathematics 4052 syllabus (exams from 2026) checked 2025-11-30 - scope unchanged; remains the reference for these notes.

Quick reference

Mean of grouped data: $\bar{x} = \dfrac{\sum fx}{\sum f}$

Reviewed by

Marcus Pang·Managing Director (Maths)

Class	Frequency	Cumulative frequency	Midpoint	$fx$
0-20	6	6	10	60
20-40	12	18	30	360
40-60	10	28	50	500
60-80	7	35	70	490
80-100	5	40	90	450
Total	40			1860

Step	What to write	Why it matters	Common trap
Find each midpoint	Add the lower and upper class limits, then divide by $2$ .	The midpoint stands in for every value in that class.	Using the upper class limit as if every value is at the top of the class.
Multiply by frequency	Calculate $fx$ for each class.	A class with more values should contribute more to the estimated total.	Adding the midpoints without weighting by frequency.
Add the estimated totals	Find $\sum fx$ .	This estimates the total of all raw values.	Treating $\sum f$ and $\sum fx$ as the same type of total.
Divide by total frequency	Use $\bar{x} = \dfrac{\sum fx}{\sum f}$ .	The denominator is the number of observations.	Dividing by the number of classes instead of total frequency.

Question focus	Better statistic	Why it fits	Common trap
Typical value with no obvious outlier	Mean or median	Mean uses every value; median gives the middle position.	Quoting all three averages without saying what they show.
Typical value when the data is skewed or has an outlier	Median	Median is less affected by one very large or very small value.	Letting one outlier pull the mean and calling it typical.
Consistency or spread of the middle half	IQR	It compares the central 50% of the data.	Using range when the question asks about consistency.
Overall spread including extremes	Range	It uses the smallest and largest values.	Treating range as typical spread when the extremes are unusual.
Calculator comparison of raw datasets	Standard deviation	Smaller standard deviation means values are more tightly clustered around the mean.	Saying lower standard deviation means lower scores; it means less spread.

Ingredient	What it means	For the 90th percentile example
Lower boundary $L$	Start of the class that contains the target position	$80$
Previous cumulative frequency $c$	Number of values before that class	$35$
Class frequency $f$	Number of values inside that class	$5$
Class width $w$	Width of the class interval	$20$

Task wording	What to write first	When to use the line	Common trap
"Describe the correlation"	Direction and strength, such as strong positive correlation	Do not calculate a prediction unless asked.	Writing a causal sentence instead of a pattern sentence.
"Estimate the value when x = ..."	Check that the x-value lies inside the observed range	Use interpolation from the line of best fit.	Reading from a point on the scatter plot instead of the trend line.
"Predict beyond the data"	State that the estimate is unreliable or risky	Use only if the question insists, and flag extrapolation.	Treating the straight-line trend as guaranteed outside the data range.
"Explain why y increases"	Mention correlation, then say another factor could be involved	The graph alone cannot prove a cause.	Saying x causes y just because the points slope upward.

IP EMaths Notes (Upper Sec, Year 3-4): 15) Statistics and Data Handling

Quick reference

Sources

Building organised tables

Example table layout

Grouped mean midpoint checkpoint

Measures of central tendency

Measures of spread

Measure-choice checkpoint

Worked example - Cumulative frequency percentile

Cumulative frequency class checkpoint

Grouped-data interpolation checkpoint

Worked example - grouped data (mean, median, quartiles)

Worked example - comparing box plots

Worked example - scatter plot and correlation

Scatter-plot prediction checkpoint

Practice Quiz

Try this

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