Problem 4 - Basic Engineering Mathematics

Question

The number of issues of tools or materials from a store in a factory is observed for seven, one-hour periods in a day, and the results of the survey are as follows: \(\begin{array}{lccccccc}\text { Period } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \text { Number of issues } & 34 & 17 & 9 & 5 & 27 & 13 & 6\end{array}\) Present these data on a vertical bar chart.

Step-by-Step Solution

Answer

Create a vertical bar chart with periods along the x-axis and number of issues on the y-axis, each bar's height reflecting the number of issues.

Step 1: Understand the Data

You have seven periods and the corresponding number of issues of tools or materials for each period. The data is: Period 1: 34, Period 2: 17, Period 3: 9, Period 4: 5, Period 5: 27, Period 6: 13, Period 7: 6.

Step 2: Set Up the Bar Chart Axes

Determine the chart axes. The horizontal axis (x-axis) will represent the time periods (Period 1 to Period 7), while the vertical axis (y-axis) will represent the number of issues. Select an appropriate scale for the y-axis that accommodates the highest number of issues, which is 34.

Step 3: Draw the Vertical Bars

Draw a vertical bar for each period. Height of each bar corresponds to the number of issues. For example, draw a bar for Period 1 that reaches up to 34 on the y-axis, a bar for Period 2 reaching 17, and so on for all periods.

Step 4: Label the Chart

Label the x-axis with each period number and the y-axis with 'Number of Issues'. Add a title to the chart, such as 'Number of Issues per Period'. Ensure each bar is properly spaced and labeled with its respective period.

Key Concepts

Data Visualization

Data visualization is a powerful tool used to convert raw data into a pictorial or graphical format. By displaying data visually, complex datasets become easier to understand. One of the common methods to visualize data is through bar charts, which are ideal for displaying categorical data. In the factory example, each period of tool issues represents a category.

Here's how you can create an effective data visualization with your dataset:

• Identify the variables: The x-axis represents time periods, while the y-axis shows the number of issues.
• Select a type of graph: Bar charts are great for comparing quantities across categories.
• Choose a scale: Ensure that the y-axis scale captures the highest and lowest values for better readability.

Through visual representation, viewers quickly grasp the fluctuation in the number of issues over different periods. This can assist in identifying trends or outliers for further analysis or decision-making in the engineering process.

Graphical Representation

Graphical representation refers to using visuals to illustrate data. In the context of the exercise, a vertical bar chart serves this purpose well. Bar charts are beneficial in showing comparisons among discrete categories and allowing viewers to digest information at a glance.

When constructing a bar chart, certain elements ensure clarity and effectiveness:

• Axis Designation: The horizontal axis represents different categories or time periods, and the vertical axis represents the metric of interest.
• Bar Length: The height or length of each bar correlates directly with the data values.
• Labeling: Ensure both axes are labeled clearly, and each bar is marked accordingly.

These components construct a straightforward picture of the data distribution. In engineering, precise graphical representations aid in identifying issues, analyzing patterns, and understanding complex scenarios better.

Statistics in Engineering

Statistics in engineering involves the collection and analysis of data to make informed decisions, solve problems, and optimize processes. In engineering contexts, understanding how to effectively visualize data is crucial. Bar charts, for instance, provide insights into production performance, as seen with the number of tool issues in each period.

Implementing statistics in engineering involves:

• Data Collection: Gather data accurately over specific periods or test cycles.
• Data Analysis: Identify statistical measures like mean, median, and mode to ascertain trends.
• Interpretation: Use visualization tools such as bar charts to communicate findings effectively.

A well-constructed statistical analysis informs engineers about process efficiencies, potential bottlenecks, or areas for improvement. By using such graphic tools, engineers can better visualize the tangible effects of changes in procedures or materials, thus enhancing process optimization.