← Data Analytics from Scratch: SQL, Spreadsheets and Metrics
Lesson
Shares, percentages — percent vs percentage points
Learner can compute a share and a percent change and can correctly distinguish a change in percentage points from a relative percent change.
Percentages and percentage points: spot the difference
Percentages and percentage points: spot the difference
A share is simply a part divided by the whole: share = part / whole. Multiply by 100 to express it as a percentage. Example: 24 out of 80 customers renewed their subscription. Share = 24/80 = 0.30. Percentage = 30%. Straightforward.
Percent change measures how much a quantity has grown or shrunk relative to its starting point: percent change = (new − old) / old × 100%. Example: revenue was 200 last quarter and 250 this quarter. Change = (250−200)/200 × 100% = 25%.
Now for the classic trap. A website's conversion rate rose from 4% to 5%. In absolute terms this is a change of +1 percentage point (pp) — you simply subtract: 5−4 = 1 pp. In relative terms it is a change of +25%: (5−4)/4 × 100% = 25%. Both statements are true, but they sound completely different. A headline reading 'conversion up 25%!' is more dramatic than 'up 1 pp' — yet both describe the exact same event.
A second trap: beware percentages when the base is very small. If 2 people had a side effect last year and 4 people do this year, that is indeed +100% — but the absolute change is just 2 cases. Always pair a relative figure with its absolute base so the reader can judge the scale. Professional analysts always specify: are we talking percentage points or relative percent change?
Lesson notes
Percentages and percentage points: spot the difference
A share is simply a part divided by the whole: share = part / whole. Multiply by 100 to express it as a percentage. Example: 24 out of 80 customers renewed their subscription. Share = 24/80 = 0.30. Percentage = 30%. Straightforward.
Percent change measures how much a quantity has grown or shrunk relative to its starting point: percent change = (new − old) / old × 100%. Example: revenue was 200 last quarter and 250 this quarter. Change = (250−200)/200 × 100% = 25%.
Now for the classic trap. A website's conversion rate rose from 4% to 5%. In absolute terms this is a change of +1 percentage point (pp) — you simply subtract: 5−4 = 1 pp. In relative terms it is a change of +25%: (5−4)/4 × 100% = 25%. Both statements are true, but they sound completely different. A headline reading 'conversion up 25%!' is more dramatic than 'up 1 pp' — yet both describe the exact same event.
A second trap: beware percentages when the base is very small. If 2 people had a side effect last year and 4 people do this year, that is indeed +100% — but the absolute change is just 2 cases. Always pair a relative figure with its absolute base so the reader can judge the scale. Professional analysts always specify: are we talking percentage points or relative percent change?