Weighted mean · 5 marks

Small-group project: Make a group of 3–4 students. Choose one scenario to design a custom rating scheme by assigning appropriate weights: (a) shopping experience at a cloth store, (b) travel experience in a bus, (c) tourism experience of a nearby tourist spot, (d) clinic/hospital experience

(i) Discuss and arrive at 4–6 aspects to rate. For each aspect chosen, justify why it matters for an overall experience.
(ii) Discuss and decide the relative weights and justify.
(iii) Collect or imagine ratings from at least 10 people on a scale of 1–5 (5 being very good).
(iv) Compute each individual rating. Compute the overall average across individuals.
(v) Make a 100% stacked bar chart using your data.
(vi) Write a short note on the observations and inferences, what your rating system captures well and what it misses.

Answer: Model answer for (d) a clinic: aspects cleanliness, waiting time, doctor’s care, staff behaviour, cost with weights 2 : 3 : 4 : 2 : 1. Each person’s rating = 2C + 3W + 4D + 2S + 1K12; for 10 sample people these range from 2.42 to 4.42 and the overall average is 435120 ≈ 3.63.

Step-by-step solution

Given: Scenario chosen for the model answer: (d) clinic/hospital experience

Idea: A custom rating is a weighted mean of the aspect ratings. The weights say how much each aspect matters; the overall average across people is the mean of the individual weighted ratings.

(i) Discuss and arrive at 4–6 aspects to rate. For each aspect chosen, justify why it matters for an overall experience.

Cleanliness (prevents infection), waiting time (patients are unwell and time matters), doctor’s care (the main purpose of the visit), staff behaviour (comfort and guidance), cost (affordability).1 mark

Cleanliness, waiting time, doctor’s care, staff behaviour, cost

(ii) Discuss and decide the relative weights and justify.

Weights 2 : 3 : 4 : 2 : 1 (total 12). Doctor’s care gets the most (4) because treatment is why people come; waiting time next (3); cleanliness and staff 2 each; cost 1, as a government clinic charges little.1 mark

2 : 3 : 4 : 2 : 1

(iii) Collect or imagine ratings from at least 10 people on a scale of 1–5 (5 being very good).

Sample ratings of 10 people (with each person’s weighted rating):

Person	Clean (2)	Wait (3)	Doctor (4)	Staff (2)	Cost (1)	Rating
P1	4	3	5	4	3	4812 = 4.00
P2	5	2	4	4	2	4212 = 3.50
P3	3	2	4	3	4	3812 = 3.17
P4	4	4	5	5	3	5312 = 4.42
P5	5	3	5	4	2	4912 = 4.08
P6	2	1	3	3	4	2912 = 2.42
P7	4	3	4	4	3	4412 = 3.67
P8	3	2	5	4	3	4312 = 3.58
P9	5	4	4	5	2	5012 = 4.17
P10	4	2	4	3	3	3912 = 3.25

½ mark

Ratings of 10 people as in the table

(iv) Compute each individual rating. Compute the overall average across individuals.

Individual rating = 2C + 3W + 4D + 2S + 1K12. For P1: 8 + 9 + 20 + 8 + 312 = 4812 = 4.00. All ten: 4.00, 3.50, 3.17, 4.42, 4.08, 2.42, 3.67, 3.58, 4.17, 3.25.1 mark
Overall average = 48 + 42 + 38 + 53 + 49 + 29 + 44 + 43 + 50 + 3912 × 10 = 435120 ≈ 3.63.½ mark

Individual ratings 2.42 to 4.42; overall ≈ 3.63

(v) Make a 100% stacked bar chart using your data.

For each aspect, find the share of 5★, 4★, 3★, 2★ and 1★ ratings among the 10 people (each person = 10%) and draw one 100% bar per aspect (diagram).½ mark

One 100% bar per aspect (see the diagram)

(vi) Write a short note on the observations and inferences, what your rating system captures well and what it misses.

Doctor’s care is rated highly (all 3 or more), but waiting time is poor (half gave 2 or less), pulling the overall score down. The system captures what patients value most, since doctor’s care counts 4 times as much as cost. It misses things like distance, medicine availability and how serious the illness was, and 10 people is a small sample.½ mark

Doctor good, waiting poor; captures priorities, misses some aspects and has a small sample

Model answer (clinic): aspects cleanliness, waiting time, doctor’s care, staff behaviour and cost with weights 2 : 3 : 4 : 2 : 1; individual weighted ratings from 2.42 to 4.42; overall average about 3.63; doctor’s care is the strength and waiting time the weakness. Your group’s answer will depend on its own choices and data.

Check: Weights add to 12, so each individual rating is between 1 and 5 ✓; the overall average 3.63 lies between the lowest (2.42) and highest (4.42) individual ratings ✓.

Answer to write in the exam

(i)

Cleanliness: hygiene and safety

Waiting time: patients are unwell

Doctor’s care: main purpose of visit

Staff behaviour: comfort and help

Cost: affordability

(ii)

Weights: cleanliness 2, waiting 3, doctor 4, staff 2, cost 1 (sum 12)

Doctor’s care matters most; cost least for a low-fee clinic

(iii)

10 sets of ratings (1–5) collected for the 5 aspects (see table)

(iv)

Rating = 2C + 3W + 4D + 2S + K12

P1 = 4812 = 4.00, …, P10 = 3912 = 3.25

Overall = 435120 = 3.63

∴ Overall average rating ≈ 3.63

(v)

Each person = 10% of a bar

One bar per aspect, split by 5★ to 1★ shares

(vi)

Doctor’s care rated high; waiting time rated low

Weights reflect what patients value most

Misses medicines, distance; sample of 10 is small

Common mistakes that cost marks

Dividing the weighted sum by the number of aspects (5) instead of the sum of the weights (12).
Giving weights without reasons; the project asks you to justify them.
Drawing the 100% chart with bars of different lengths.

How this can come in the exam

Case-based (4 marks)

A bus service is rated on punctuality, comfort and fare with weights 3 : 2 : 1. Two passengers rate it (4, 3, 5) and (2, 4, 4).
(i) Find each passenger’s rating. (ii) Find the average rating. (iii) Which aspect affects the rating most? (iv) If punctuality improves by 1 point for both passengers, by how much does the average rise?

Show answer

(i) 12 + 6 + 56 = 3.83 and 6 + 8 + 46 = 3 (1 mark). (ii) 23 + 1812 = 4112 ≈ 3.42 (1 mark). (iii) Punctuality (weight 3) (1 mark). (iv) Each rating rises by 36 = 0.5, so the average rises by 0.5 (1 mark).

Try one yourself

A cloth store is rated on variety, price and service with weights 2 : 2 : 1. A customer gives 5, 3, 4. Find her rating.