This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Understand the given data. The table shows customer ratings for Thandi's Fashion Outlet, where 1 is poor and 5 is excellent. The "Number of customers (frequency)" column indicates how many customers gave each rating. | Rating (x) | Number of customers (f) | | :--------- | :---------------------- | | 1 | 1 | | 2 | 3 | | 3 | 8 | | 4 | 12 | | 5 | 6 | | Total | 30 | Step 2: Calculate the MEAN customer rating (Question 3.1). The formula for the mean (x) of grouped data is x = ( (x · f))/( f). First, calculate x · f for each rating: • 1 × 1 = 1 • 2 × 3 = 6 • 3 × 8 = 24 • 4 × 12 = 48 • 5 × 6 = 30 Next, sum the (x · f) values: (x · f) = 1 + 6 + 24 + 48 + 30 = 109 The total number of customers ( f) is 30. Now, calculate the mean: x = (109)/(30) x ≈ 3.633 The mean customer rating is 3.63. Step 3: Determine the MEDIAN customer rating (Question 3.2). The median is the middle value in an ordered dataset. Since there are 30 customers (an even number), the median will be the average of the 15th and 16th values. To find the position, we can use cumulative frequency: • Rating 1: 1 customer (1st value) • Rating 2: 3 customers (2nd to 4th values) • Rating 3: 8 customers (5th to 12th values) • Rating 4: 12 customers (13th to 24th values) • Rating 5: 6 customers (25th to 30th values) The 15th value falls within the "Rating 4" category. The 16th value also falls within the "Rating 4" category. Therefore, the median is 4. The middle positions are the 15th and 16th values. The median customer rating is 4. Step 4: State the MODE of the customer ratings (Question 3.3). The mode is the value that appears most frequently in the dataset. From the table: • Rating 1: 1 customer • Rating 2: 3 customers • Rating 3: 8 customers • Rating 4: 12 customers • Rating 5: 6 customers The rating with the highest frequency is 4, with 12 customers. The mode of the customer ratings is 4. Step 5: Address Question 3.4. Mr Dlamini wants to describe the service in his monthly report to give the most positive impression. • Mean = 3.63 • Median = 4 • Mode = 4 Both the median and the mode are 4, which is higher than the mean of 3.63. To give the most positive impression, Mr Dlamini should choose the median or the mode. Mr Dlamini should choose the median or mode (both are 4) to describe the service, as these values are higher than the mean (3.63) and indicate a more positive customer experience. Choosing a higher average creates a more favorable impression of the service quality. What's next?