100% stacked bar charts · 4 marks

Decision Dilemma:

(i) Which of the plays would you choose to watch based on the following chart?
(ii) The corresponding stacked bar chart is shown below. Would you change your decision after looking at this chart? Why/Why not? Discuss.

Answer: (i) Play A or Play B: about 71% of their viewers gave 4 or 5 stars and few gave 1 star; Play C splits opinion (about 40% gave 5★ but a third gave 1★). (ii) Many would switch to Play B: it has about 925 ratings against about 210 for A, so its good rating is much more reliable. Play C still splits opinion.

Step-by-step solution

Idea: A 100% chart shows how opinion is divided but hides how many people rated. A stacked chart shows the numbers, which tells us how trustworthy each share is.

(i) Which of the plays would you choose to watch based on the following chart?

Read the shares: A and B each have about 71% of ratings at 4★ or 5★ and only about 11–12% at 1★. C has the largest 5★ share (about 39%) but also about 33% at 1★: people either loved it or disliked it.1 mark
Average ratings from the shares: A ≈ 3.7, B ≈ 3.7, C ≈ 3.2. A safe choice is Play A (or B, which is almost the same); someone who enjoys bold, unusual shows might gamble on C.1 mark

Play A (or B); C is risky

(ii) The corresponding stacked bar chart is shown below. Would you change your decision after looking at this chart? Why/Why not? Discuss.

Numbers of ratings: A ≈ 210, B ≈ 925, C ≈ 380. B’s shares come from more than four times as many people as A’s.1 mark
Since A and B have almost the same shares, the one rated by far more people (B) gives the more trustworthy picture, so many would change to Play B. (A few might keep A: its shares are fine, and fewer ratings does not mean it is worse.) C’s large number of 1★ ratings is confirmed.1 mark

Yes, many would choose Play B: its rating is based on about 925 viewers

(i) Play A (or B), since about 71% of viewers rated them 4 or 5 stars, while Play C divides opinion. (ii) The stacked chart shows Play B was rated by about 925 people and Play A by only about 210, so B’s similar rating is more reliable; many would switch to Play B.

Check: Average from counts: A ≈ 5 × 60 + 4 × 89 + 3 × 30 + 2 × 5 + 1 × 26210 ≈ 3.72; B ≈ 3421924 ≈ 3.70; C ≈ 1195379 ≈ 3.15 (readings from the chart are approximate).

Answer to write in the exam

(i)

A and B: ≈ 71% gave 4★ or 5★; ≈ 11–12% gave 1★

C: ≈ 39% gave 5★ but ≈ 33% gave 1★

∴ Choose Play A (or B)

(ii)

Number of ratings: A ≈ 210, B ≈ 925, C ≈ 380

A and B have similar shares; B’s are based on far more viewers

∴ Change to Play B (more reliable rating)

Common mistakes that cost marks

Choosing C only because it has the biggest 5★ piece, ignoring its very big 1★ piece.
Thinking B is the most popular play in (i). The 100% chart cannot show how many people rated.
Saying B is better because its bar is longer in (ii). A longer bar means more ratings, not better ratings.

How this can come in the exam

Assertion–Reason (1 mark)

Assertion (A): From a 100% stacked bar chart of ratings we cannot tell which product was rated by more people.
Reason (R): Every bar in a 100% stacked bar chart has the same length.

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

(A) Both A and R are true, and R is the correct explanation of A.
Equal lengths hide the totals, so R explains A.

Try one yourself

Restaurant X: 80% of 10 ratings are 5★. Restaurant Y: 70% of 500 ratings are 5★. Which rating would you trust more, and why?