Select the correct graph. The following table shows the monthly defect rate for a product at a manufacturing company.
| Month | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| :----------------------------------- | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: |
| Number of Defects (per 1,000 units) | 18 | 21 | 22 | 25 | 28 | 25 | 24 | 18 | 20 | 21 | 26 | 28 |
The production manager is going to present this information to the company's board of directors. Which graph should the manager use to best emphasize that the number of defects has remained relatively consistent throughout the year?
Answer (2)
Analyze the data to understand the range and central tendency of defect rates.
Consider a line graph to visualize the trend of defect rates over time.
Consider a bar graph to compare the defect rates of different months.
Choose the graph that minimizes the visual fluctuations and highlights the relatively stable nature of the defect rates, which is a line graph.
Explanation
Understanding the Problem The problem asks us to determine which type of graph best emphasizes the consistency of the defect rate throughout the year. We are given the monthly defect rates for a product at a manufacturing company in a table.
Choosing the Right Graph Type To emphasize the consistency of the defect rate, we need to choose a graph that minimizes visual fluctuations and highlights the relatively stable nature of the data. A line graph is suitable for showing trends over time. A bar graph is good for comparing values across different categories (in this case, months).
Analyzing the Data The range of defect rates is 28 − 18 = 10 . The mean defect rate is 23, and the median defect rate is 23. These values give us an idea of the central tendency and spread of the data.
Comparing Graph Visuals A line graph connecting the data points would show the fluctuations in the defect rate from month to month. However, if the goal is to emphasize consistency, a line graph might visually exaggerate the variations. A bar graph would show the defect rate for each month as a separate bar. This could also emphasize the differences between months.
Determining the Best Graph To best emphasize that the number of defects has remained relatively consistent throughout the year, we should choose a graph that minimizes the visual fluctuations. A line graph is more appropriate to show the trend, but it can also highlight the variations. A bar graph can also emphasize the differences between months. In this case, a line graph would be the best choice to show the trend of the defect rates over the year.
Examples
Consider a scenario where a company wants to showcase the stability of its stock price over a year to potential investors. Using a line graph, the company can visually represent the stock price fluctuations each month. If the line remains relatively flat, it emphasizes the stock's consistent performance, reassuring investors of its stability. This approach is also applicable in fields like environmental science, where consistent pollution levels need to be demonstrated.
A bar graph is the best choice for the production manager to emphasize that the defect rates have remained consistent throughout the year. While a line graph shows trends, it may exaggerate minor fluctuations, while a bar graph presents a clearer visual of stability. Therefore, the bar graph minimizes visual fluctuations, making it appropriate for this purpose.
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