Read values carefully, compare like with like and explain what the evidence actually supports.
Lesson 05 · StatisticsYour learning goal
Interpret values and changes, compare representations and distinguish supported conclusions from overclaims.
Read the frame before the pattern
Check the title, source, sample, dates, units, axes and legend before interpreting the shape. A rising line could represent total sales, sales per person or a running total. Those are different quantities. A cumulative total normally rises when new positive amounts are added, even if the amount added each week is falling.
Difference, ratio and percentage change
An increase from 40 to 50 is a difference of 10. The new value is 1.25 times the old value, and the percentage increase is 10 ÷ 40 × 100 = 25%. The original value is the denominator for percentage change. Moving from 40% to 50% is an increase of 10 percentage points, as well as a 25% relative increase.
Compare the same thing
Two groups may differ in size, observation time or definitions. A larger school may record more absences simply because it has more students. Comparing absence rates can answer a different and fairer question. State the denominator, check whether it is comparable, and avoid assuming that rates answer every possible question better than counts.
Describe uncertainty honestly
A point between gridlines may only support an estimate unless exact values are labelled or available in a table. A graph of five school days does not establish a long-term pattern. An unusually high observation deserves checking, but removing it without a reason changes the evidence. Describe what is known and what remains uncertain.
Explore · predict, test, explain
Make your thinking visible.
Graph Lab
Enter one label and value per line, separated by a comma. This tool supports 2–12 non-negative values. The table and graph always use the same data.
Line graphs use equally spaced positions here: use observations at equal time intervals. Do not use a line to connect unrelated categories. Circle graphs require a positive total.
Worked examples
Follow the reasoning.
The same rise, two descriptions
A club grows from 40 members to 50 members.
Absolute increase: 50 − 40 = 10 members.
Percentage increase: 10 ÷ 40 × 100 = 25%.
A bar drawn from 35 has visible lengths 5 and 15; that visible 3:1 ratio is not the true 50:40 ratio.
Comparing two schools
School A records 30 absences among 600 students; School B records 20 among 200 students on the same day.
A has more recorded absences: 30 compared with 20.
The shares are 5% for A and 10% for B.
Answer the question precisely: count and share produce different comparisons.
Guided Practice
Build an explanation.
A score rises from 60 to 75. Find the change and percentage increase.
Give me a hint
Divide the increase by the starting value.
Compare a worked response
The change is 15 points. The relative increase is 15 ÷ 60 × 100 = 25%. A 15-point rise is not automatically a 15% increase.
A line rises during the week a poster campaign runs. Has the campaign been proved effective?
Give me a hint
Consider other changes during that week and whether a comparison group exists.
Compare a worked response
The observations are consistent with improvement during the campaign, but they do not establish causation. Attendance, weather, measurement or other initiatives could also matter.
Independent Practice
Test the idea, then check your reasoning.
Feedback explains your chosen response. These activities are practice, not a school mark.
Connections
Use it beyond this page.
Compare a headline with its graph. Rewrite the headline using a measured quantity, a named group and a stated time period.
Take it further
Explain why a 20% increase followed by a 20% decrease does not return a value to its starting point. Use a starting value of 100 and show both calculations.