The 100% stacked bar below compares the proportion of flowers blooming in Fatima’s garden and Naveen’s garden across seasons. Which of the following statements can be inferred from this chart?
(Hint: Find out the blooms per season in each garden if both the gardens had the same total number of blooms over the year. Similarly find out what happens if the totals are very different.)
- (i) In Fatima’s garden, there were more blooms in the summer than in the monsoon.
- (ii) In summer, Fatima’s garden had more blooms than Naveen’s garden.
- (iii) In winter, Fatima’s garden had fewer blooms than Naveen’s garden.
- (iv) The total number of flowers, across seasons, is the same in both gardens but it varies in each season.
Step-by-step solution
Idea: Each bar is that garden’s own total, taken as 100%. Comparing pieces within one bar compares real numbers; comparing pieces across bars does not, because the two totals may be different.
(i) In Fatima’s garden, there were more blooms in the summer than in the monsoon.
- Same garden, same total: 50% of her flowers is more than 30% of the same flowers. Can be inferred (true).1 mark
(ii) In summer, Fatima’s garden had more blooms than Naveen’s garden.
- 50% of Fatima’s total vs 40% of Naveen’s total. If the totals are 210 and 120 (Case 1): 105 > 48. If the totals are 180 and 240 (Case 2): 90 < 96. It can go either way, so it cannot be inferred.1 mark
(iii) In winter, Fatima’s garden had fewer blooms than Naveen’s garden.
- 20% of Fatima’s total vs 35% of Naveen’s. In Case 1 both are 42 (not fewer); in Case 2, 36 < 84. Without the totals we cannot tell, so it cannot be inferred.1 mark
(iv) The total number of flowers, across seasons, is the same in both gardens but it varies in each season.
- Every bar in a 100% chart has the same length whatever its total, so the chart says nothing about whether the totals are equal (Case 1 has 210 and 120; Case 2 has 180 and 240). Cannot be inferred.1 mark
Check: Case 1: 105210 = 50%, 63210 = 30%, 42210 = 20%; 48120 = 40%, 30120 = 25%, 42120 = 35% ✓. Case 2: 90180 = 50%, 96240 = 40%, 84240 = 35% ✓. (The chart gives Naveen 25% in monsoon and 35% in winter.)
Answer to write in the exam
(i)
Fatima: summer 50%, monsoon 30% of the same total
∴ (i) can be inferred
(ii)
Case 1: Fatima 105, Naveen 48 (Fatima more)
Case 2: Fatima 90, Naveen 96 (Naveen more)
∴ (ii) cannot be inferred
(iii)
Case 1: Fatima 42, Naveen 42 (equal)
Case 2: Fatima 36, Naveen 84
∴ (iii) cannot be inferred
(iv)
100% bars always have equal length
Totals could be 210 and 120, or 180 and 240
∴ (iv) cannot be inferred
Common mistakes that cost marks
- Accepting (ii) because 50% is more than 40%. Percentages of different totals cannot be compared as numbers of flowers.
- Thinking equal bar lengths mean equal totals, as in (iv).
- Mixing up Naveen’s monsoon (25%) and winter (35%) pieces; read the colours from the legend.
How this can come in the exam
A 100% stacked bar shows that 60% of School P’s students and 45% of School Q’s students walk to school. Which conclusion is valid?
- More students walk in P than in Q
- P has more students than Q
- In P, more students walk than do not walk
- Fewer students walk in Q than in P
Show answer
(C) In P, more students walk than do not walk
Within P, 60% walk and 40% do not, so more walk. The others compare different totals.
Give totals for which 40% of Garden X’s flowers is more than 60% of Garden Y’s flowers.
Show answer
Take X = 300 and Y = 100: 40% of 300 = 120 > 60% of 100 = 60 (any totals with 0.4X > 0.6Y; 2 marks).Try one yourself
A 100% bar shows 70% of a shop’s sales in March were online and 55% in April. Can we say online sales fell in April?
Show answer
No. If total sales in April were much larger, 55% of it could be more than 70% of March’s total. We only know the share fell.
More questions like this
- 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? - 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?