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Stacked bar charts · 5 marks

Now, use the stacked bar chart to answer the five questions shown earlier. Is it possible? Is it easy? If not, what made it harder than before?

  1. 1. Which family spent the least on housing?
  2. 2. Which family spent the most on healthcare?
  3. 3. Approximately how much did Family A spend on education?
  4. 4. Which category did Family B spend most on?
  5. 5. Did Family A spend more on food or on healthcare?
Expenditure of three families in a monthHousingFoodEducationTransportationHealthcareRecreationFamily AFamily BFamily C02000400060008000Expenditure (₹)
Answer: It is possible but harder. The answers are the same (1. Family C, 2. Family A, 3. about ₹1300, 4. Housing, 5. Healthcare), but only the first piece of each bar starts at 0; the other pieces start at different places, so their lengths must be worked out as end − start and compared without a common base.

Step-by-step solution

Given: Average weekly expenditure (₹) of three families:
HousingFoodEducationTransportationHealthcareRecreation
Family A19401700128012001770535
Family B175015461500128012100
Family C9501700154014001300150

Idea: In a stacked bar, the length of a piece (not where it ends) shows its amount. Pieces other than the first do not start at 0, and the same category starts at a different point in each bar.

1. Which family spent the least on housing?

  1. Housing is the first piece, which starts at 0 in every bar, so this is still easy: Family C’s housing piece ends first (near 950). Family C.1 mark
Family C (easy, since housing starts at 0)

2. Which family spent the most on healthcare?

  1. The healthcare pieces start at different points (about 6120, 6080 and 5590). Their lengths: A ≈ 7890 − 6120 = 1770, B ≈ 7290 − 6080 = 1210, C ≈ 6890 − 5590 = 1300. Family A. Harder, because the lengths must be judged without a common start.1 mark
Family A (harder: pieces start at different points)

3. Approximately how much did Family A spend on education?

  1. Family A’s education piece starts at about 3640 and ends at about 4920: 4920 − 3640 ≈ ₹1300 (exactly ₹1280). We must subtract, which is harder than reading one column.1 mark
About ₹1300

4. Which category did Family B spend most on?

  1. Compare the lengths of the pieces in Family B’s bar: housing ≈ 1750, food ≈ 1550, education ≈ 1500, transport ≈ 1280, healthcare ≈ 1210. Housing is the longest, but housing, food and education are close and sit side by side, so it is hard to be sure from the chart alone.1 mark
Housing (hard to be sure; three pieces are similar)

5. Did Family A spend more on food or on healthcare?

  1. Food ≈ 3640 − 1940 = 1700 and healthcare ≈ 7890 − 6120 = 1770. Healthcare, but the pieces are far apart in the bar and differ by only ₹70, so the chart alone makes this very hard. Before, the two columns stood side by side from 0.1 mark
Healthcare (very hard to tell from the stacked bar)
It is possible but not easy. Except for the first piece (housing), the pieces do not begin at 0, and a category begins at a different place in each family’s bar, so lengths have to be found by subtraction and compared without a common base. The stacked bar is better for totals, the cluster charts for comparing individual categories.

Answer to write in the exam

1.

Housing pieces: A ends ≈ 1940, B ≈ 1750, C ≈ 950

∴ Family C spent the least on housing

2.

Healthcare lengths: A ≈ 1770, B ≈ 1210, C ≈ 1300

∴ Family A spent the most on healthcare

3.

Education piece of A: from ≈ 3640 to ≈ 4920

Length ≈ 4920 − 3640 = 1280

∴ About ₹1300

4.

Family B pieces: 1750, 1546, 1500, 1280, 1210

∴ Family B spent most on housing

5.

Food ≈ 1700, healthcare ≈ 1770

∴ Family A spent more on healthcare

Common mistakes that cost marks

  • Reading where a piece ends as its value (for example, saying Family A spent ₹4920 on education).
  • Judging pieces by their position instead of their length.
  • Saying the stacked chart cannot answer these questions at all. It can; it is just harder.

How this can come in the exam

Assertion–Reason (1 mark)

Assertion (A): In a stacked bar chart, it is easy to compare the first pieces of different bars.
Reason (R): The first piece of every bar starts at 0.

  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
Show answer

(A) Both A and R are true, and R is the correct explanation of A.
A common starting point makes comparison easy, so R explains A.

Try one yourself

In a stacked bar, a piece starts at 2400 and ends at 3150. What amount does it show?

Show answer

Length = 3150 − 2400 = 750.

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