O-Level E-Math and SEC G3 Mathematics K310
S1: Data handling and analysis
Choose suitable summaries and representations, then interpret spread, centre, trends, and possible limitations.
Core notes
Statistics turns collected data into representations and summaries. A sound interpretation considers centre, spread, shape and data quality rather than quoting one statistic in isolation.
Collecting and representing data
Classify and tabulate data with clear categories and frequencies. Tables, bar graphs, pictograms, line graphs, pie charts, dot diagrams, equal-width histograms, stem-and-leaf diagrams, cumulative-frequency diagrams and box plots serve different purposes. Choose a representation that preserves the feature being studied.
Inference and misleading displays
An inference should be supported by visible evidence and limited to the sampled population. Truncated axes, unequal visual scales, distorted pictures or omitted context can exaggerate differences. State precisely how the display could mislead.
Measures of centre
Mean uses every value but is affected by extreme observations. Median is resistant to extremes, while mode identifies the most frequent value or category. For grouped data, use class midpoints to estimate the mean.
Position and spread
Quartiles and percentiles locate data within an ordered distribution. Range and interquartile range measure spread directly; standard deviation measures typical distance from the mean. Compare two data sets using both mean and standard deviation and refer to the context.
Formulae and methods
| Relationship | Use |
|---|---|
| Find a frequency-weighted or grouped mean. | |
| Find the population standard deviation for frequency data. | |
| Measure the spread of the middle half of the data. |
Worked examples
Example 1: Values have frequencies . Find the mean.
- Compute .
- Compute .
- Calculate .
Answer: The mean is .
Example 2: Class A has mean and standard deviation ; Class B has mean and standard deviation . Compare them.
- The equal means indicate the same average score.
- Compare spread using standard deviation.
- The smaller standard deviation means Class A is more consistent around the mean.
Answer: The classes have the same mean, but Class A's scores are less spread out.
Chapter checkpoint
- Identify the data type, collection method and representation before interpreting.
- Choose a measure of centre and spread that fits the distribution and question.
- Compare data sets in context using both centre and spread, and inspect whether the display could mislead.
Exam traps and retrieval check
Avoid these traps
- Comparing two data sets using only their means.
- Treating a grouped-data mean as exact rather than an estimate based on midpoints.
- Describing a graph as misleading without identifying the design feature causing distortion.
Check from memory
Which centre is resistant to a large outlier?
The median.
What does a smaller standard deviation indicate?
Values are more tightly clustered around the mean.
Why is a grouped mean usually an estimate?
The exact values inside each class are replaced by the class midpoint.
Official K310 coverage
This chapter maps to 12 official outcomes: S1.1, S1.2, S1.3, S1.4, S1.5, S1.6, S1.7, S1.8, S1.9, S1.10, S1.11, S1.12. Check the official 2027 K310 syllabus for exact assessable wording and paper details.