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Stacked bar charts · 3 marks

Was it as straightforward to answer these questions as the earlier questions? Is there a visualisation that makes it simpler to answer such questions? Look at the following visualisation of the same data. Try to understand how the chart is organised and answer the three questions above.

  1. (i) Which family spent the least amount overall?
  2. (ii) Approximately how much did Family C spend overall?
  3. (iii) Approximately what percentage of Family C’s expenses were on housing?
Expenditure of three families in a monthHousingFoodEducationTransportationHealthcareRecreationFamily AFamily BFamily C02000400060008000Expenditure (₹)
Answer: No: with cluster charts we had to add six columns for each total. A stacked bar chart makes it simple, because the whole length of each bar is the family’s total. (i) Family C (shortest bar). (ii) About ₹7000. (iii) The housing piece is about one-seventh of Family C’s bar, about 13–14%.

Step-by-step solution

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

Idea: In a stacked bar chart, the parts of each family’s spending are joined end to end. So the end of the bar shows the total, and each piece’s share of the bar shows its fraction of the total.

(i) Which family spent the least amount overall?

  1. No adding is needed: the total is where the bar ends. Family C’s bar is the shortest (it ends near 7000), so Family C spent the least.1 mark
Family C

(ii) Approximately how much did Family C spend overall?

  1. Family C’s bar ends just past the 7000 mark: about ₹7000 (exactly ₹7040).1 mark
About ₹7000

(iii) Approximately what percentage of Family C’s expenses were on housing?

  1. Family C’s housing piece runs from 0 to about 950, and the whole bar is about 7000 long. 9507000 ≈ 17 ≈ 0.14, so about 13–14% (exactly 13.5%).1 mark
About 13–14%
The cluster charts made these total-based questions slow, since every column had to be added. A stacked bar chart answers them directly: Family C has the shortest bar (least spending), its total is about ₹7000, and its housing piece is about 13.5% of the bar.

Answer to write in the exam

(i)

Bar lengths: A ≈ ₹8400, B ≈ ₹7300, C ≈ ₹7000

∴ Family C spent the least overall

(ii)

End of Family C’s bar ≈ 7000 on the scale

∴ Family C spent about ₹7000

(iii)

Housing piece ≈ 950; whole bar ≈ 7040

9507040 × 100 ≈ 13.5%

∴ About 13.5% of Family C’s spending was on housing

Common mistakes that cost marks

  • Reading where a later piece ends as its value: Family C’s food piece ends at 2650, but food is 2650 − 950 = 1700. Only the first piece starts at 0; for the others, length = end − start.
  • Comparing only the first pieces instead of the full bars when asked about totals.
  • Estimating the percentage against the scale’s 8000 mark instead of against Family C’s own bar.

How this can come in the exam

MCQ (1 mark)

In a stacked bar chart of a family’s monthly spending, the total length of the bar shows

  1. the largest single expense
  2. the family’s total spending
  3. the average expense
  4. the number of categories
Show answer

(B) the family’s total spending
The pieces are joined end to end, so the bar’s length is the sum of all the expenses.

Try one yourself

In a stacked bar, a family’s food piece runs from 0 to 2500 and the whole bar ends at 10000. Roughly what percentage of its spending is on food?

Show answer

250010000 × 100 = 25%.

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