1. What does this say about the scope of the stacked bars and 100% stacked bars?
2. Given a stacked bar chart can we make a corresponding 100% stacked bar chart?
3. Given a 100% stacked bar chart can we make a corresponding stacked bar chart?
4. What kind of inferences or comparisons can be made from a stacked bar chart and in a 100% stacked bar chart?
- 1. What does this say about the scope of the stacked bars and 100% stacked bars?
- 2. Given a stacked bar chart can we make a corresponding 100% stacked bar chart?
- 3. Given a 100% stacked bar chart can we make a corresponding stacked bar chart?
- 4. What kind of inferences or comparisons can be made from a stacked bar chart and in a 100% stacked bar chart?
Answer: 1. Stacked bars show amounts (and totals); 100% stacked bars show only shares. 2. Yes: divide each piece by its bar’s total. 3. No, not without the totals: many stacked charts give the same 100% chart. 4. Stacked: compare totals and actual amounts; 100%: compare proportions within and across bars.
Step-by-step solution
Given: Fatima’s and Naveen’s 100% bars (50/30/20 and 40/25/35) fit both Case 1 (totals 210, 120) and Case 2 (totals 180, 240)
Idea: Going from amounts to percentages throws away the totals. You can always go from amounts to percentages, but not back.
1. What does this say about the scope of the stacked bars and 100% stacked bars?
- The same 100% chart fitted two very different stacked charts. So a stacked bar chart carries more information (actual numbers and totals), while a 100% stacked bar shows only how each total is divided. Each answers a different kind of question.1 mark
Stacked bars: amounts and totals. 100% stacked bars: proportions only.
2. Given a stacked bar chart can we make a corresponding 100% stacked bar chart?
- Yes. From a stacked bar we can read each piece and the total, and find piecetotal × 100 for every piece. For example, 105, 63, 42 out of 210 give 50%, 30%, 20%.1 mark
Yes
3. Given a 100% stacked bar chart can we make a corresponding stacked bar chart?
- No, not unless the totals are also given. 50%, 30%, 20% could come from 105, 63, 42 or 90, 54, 36 or any other total. If the totals are known, then yes.1 mark
No (only if the totals are also known)
4. What kind of inferences or comparisons can be made from a stacked bar chart and in a 100% stacked bar chart?
- Stacked bar: compare totals of the bars, find actual amounts of parts, compare amounts across bars (most easily for the first piece). 100% stacked bar: compare the share of each part within a bar and the shares across bars; it cannot compare actual amounts or totals.1 mark
Stacked: totals and amounts. 100%: proportions within and across bars.
A stacked bar chart shows actual amounts and totals; a 100% stacked bar chart shows only proportions. We can always turn a stacked bar chart into a 100% stacked bar chart, but not the other way round unless the totals are known. Use stacked bars for amounts and totals, 100% stacked bars for shares.
Answer to write in the exam
1.
Same 100% chart fits Case 1 and Case 2
∴ Stacked bars show actual amounts and totals; 100% stacked bars show only proportions
2.
Share = piecetotal of bar × 100
∴ Yes, a 100% stacked bar chart can always be made
3.
50%, 30%, 20% fit 105, 63, 42 and also 90, 54, 36
∴ No, not without the totals
4.
Stacked bar: totals, actual amounts of parts
100% stacked bar: proportions (shares) within and across bars, not amounts
∴ Use stacked for ‘how many’, 100% for ‘what fraction’
Common mistakes that cost marks
- Saying a 100% chart can show which garden had more flowers. It cannot; it hides the totals.
- Thinking the conversion works both ways. Percentages alone cannot give back the numbers.
- Saying stacked bars cannot show shares at all. They can, but you must divide by each total yourself.
How this can come in the exam
Assertion–Reason (1 mark)
Assertion (A): A stacked bar chart can always be converted into a 100% stacked bar chart.
Reason (R): A 100% stacked bar chart shows the totals of each bar.
- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true, but R is not the correct explanation of A.
- A is true but R is false.
- A is false but R is true.
Show answer
(C) A is true but R is false.
A is true (divide each piece by its total). R is false: a 100% chart hides the totals.
Try one yourself
A 100% stacked bar shows a class’s marks split 25% maths, 75% other subjects. Can you say how many marks were in maths? What extra fact would you need?
Show answer
No. You need the total marks. For example, if the total is 400, maths = 25% of 400 = 100.
More questions like this
- The following chart shows the time spent on different activities in a day by the average Indian. What do you notice? What do you wonder about?
- 1. What do you find interesting in the chart above? What can you infer? Discuss.
2. Do you remember the sleep time over age trend that you studied last year? Does that trend align with this chart?
3. Can you explain why the learning time of people in the age group 15 – 24 has reduced significantly compared to that of the age group 6 – 14?
4. Do adults spend about an equal amount of time in paid and unpaid work? What do you think? - What type of chart is this — a stacked bar chart or a 100% stacked bar chart?
- Do you remember the ‘What Can A Strip Say?’ activity from last year? In each strip, if we club the tiny strips belonging to each activity together, will we get a 100% stacked bar chart like the one in the figure?
- The smart watch data of 5 people was tracked from Monday to Friday. The recorded data tells us how many hours each person spent lying down, sitting, and standing or moving around, etc., as shown in the following table.