How to Calculate Mean Ratings from a Bar Chart and Make a Company Recommendation

Question

Each company a rating from 1 to 5, where 5 is the highest rating. The ratings that each company received are shown in the bar chart below. a) Calculate the mean rating that 'Waterhouse and Works' received. b) Calculate the mean rating that 'Prime Plumbing' received. c) Use your answers to parts a) and b) to decide which of the plumbing companies you would recommend. Write a sentence to explain your answer.

Accepted Answer

a) 3.2; b) 3.4; c) I would recommend Prime Plumbing, because it has a higher mean rating, indicating it received better overall customer feedback.

Answer

Step 1: Extract the frequency of each rating for Waterhouse and Works from the bar chart: Rating 1: 30, Rating 2: 20, Rating 3: 50, Rating 4: 40, Rating 5: 60 Step 2: Calculate the total rating points for Waterhouse and Works: (1×30) + (2×20) + (3×50) + (4×40) + (5×60) = 30 + 40 + 150 + 160 + 300 = 680. Calculate total number of ratings: 30+20+50+40+60=200. Mean = 680÷200 = 3.2 Step 3: Extract the frequency of each rating for Prime Plumbing from the bar chart: Rating 1: 20, Rating 2: 30, Rating 3: 10, Rating 4: 60, Rating 5: 80 Step 4: Calculate the total rating points for Prime Plumbing: (1×20) + (2×30) + (3×10) + (4×60) + (5×80) = 20 + 60 + 30 + 240 + 400 = 750. Calculate total number of ratings: 20+30+10+60+80=200. Mean = 750÷200 = 3.4 Step 5: Compare the two mean ratings: 3.4 > 3.2. Since a higher mean rating reflects better overall customer satisfaction, recommend Prime Plumbing and explain this reasoning in one sentence.