Problem 3 - Basic Engineering Mathematics

Question

The distance in miles travelled by four salesmen in a week are as shown below. \(\begin{array}{lcccc}\text { Salesmen } & P & Q & R & S \\ \text { Distance traveled (miles) } & 413 & 264 & 597 & 143\end{array}\) Use a horizontal bar chart to represent these data diagrammatically.

Step-by-Step Solution

Answer

Plot a bar extending to the distance value for each salesman on a horizontal chart.

Step 1: Understand the Data

First, we identify the data that needs to be represented in a horizontal bar chart. We have four salesmen: P, Q, R, and S, and the distances they traveled in miles: 413, 264, 597, and 143 respectively.

Step 2: Sketch the Axes

We will draw a horizontal and a vertical axis. The vertical axis (Y-axis) will represent the salesmen and the horizontal axis (X-axis) will represent the distance traveled in miles.

Step 3: Determine Scale for X-Axis

Choose a suitable scale for the X-axis. Since the maximum distance is 597 miles and the minimum is 143 miles, a scale from 0 to 600 with intervals of 100 would be appropriate.

Step 4: Plot the Bars

Draw horizontal bars for each salesman. Start with Salesman P and draw a bar extending up to 413 on the X-axis. Do the same for Q (extend to 264), R (extend to 597), and S (extend to 143).

Step 5: Label the Chart

Label each axis: 'Distance Traveled (miles)' for the X-axis and 'Salesmen' for the Y-axis. Additionally, each bar should be labeled or color-coded accordingly to indicate which salesman it represents.

Key Concepts

Data Representation

The concept of data representation is all about how we can convey information in a visual format so that it's easy to understand. In the context of a horizontal bar chart, this means taking the numerical data - in this case, the distances traveled by each salesman - and converting them into visual elements (bars) that are easy to compare and analyze at a glance.

Visual representation makes it simpler to identify trends, differences, and similarities in data without having to process long numeric tables. Each bar corresponds to a specific data point, which allows observers to quickly pinpoint who traveled the furthest or least.

• Helps in quickly understanding large datasets
• Facilitates easy comparison between data points
• Provides a clear and immediate picture of numerical data

Visualizing data through horizontal bar charts makes information more accessible, especially for viewers who might find interpreting numbers challenging.

Axes Sketching

Axes sketching is a crucial step in setting up a horizontal bar chart. The chart needs two main reference lines. First, the vertical axis, which is typically the Y-axis in these charts, will represent categories - here, the salesmen P, Q, R, and S.

The horizontal axis, or the X-axis, is reserved for the data values - in our scenario, the miles traveled by each salesman.

• Y-axis: Marks categories like people, items, etc.
• X-axis: Indicates the numerical data being represented

Before sketching the axes, determine where the labels and marks will be placed. Ensure that both axes are clearly defined with appropriate labels, helping viewers immediately understand which axis represents what.

Scale Determination

Now that the axes are set, determining the scale for the X-axis is essential. The scale is essentially the range of values that will fit the data comfortably.

First, identify the lowest and highest data points. In our problem, the distances range from 143 miles to 597 miles. Hence, a scale from 0 to 600 miles is appropriate, especially when marked in intervals of 100.

• Selects an appropriate range: 0 to maximum value (600 here)
• Defines the interval marks (e.g., 100 miles here)
• Makes sure all data points fit on the chart without squeezing them

Choosing the right scale ensures that the chart is neither too cramped nor too sparsely populated, making it both readable and visually appealing.

Chart Labeling

Proper chart labeling provides clarity and helps in data interpretation. Labeling involves marking each axis with informative titles and ensuring that individual data points — in this case, the bars representing each salesman — are easily identifiable.

For our bar chart:

• The X-axis should be labeled as 'Distance Traveled (miles)'
• Each bar should represent a salesman
• The Y-axis should be labeled as 'Salesmen'

Additional touches like color-coding each bar or placing small data labels on them can further enhance readability. Well-labeled charts make it simple for anyone to understand the represented data, even with minimal background information on the dataset.