Problem 2 - Basic Engineering Mathematics

Question

The number of television sets repaired in a workshop by a technician in six, one-month periods is as shown below. Present these data as a pictogram. \(\begin{aligned}&\text { Month } \quad \text { January February March April May June } \\\&\text { Number } \\\&\text { repaired } \quad 11 & 6 & 15 & 9 & 13 & 8\end{aligned}\)

Step-by-Step Solution

Answer

A pictogram uses TV symbols to show monthly repairs: January (5.5 icons), February (3), March (7.5), April (4.5), May (6.5), June (4).

Step 1: Analyzing the Data

The data represents the number of television sets repaired by a technician over six months. Here are the monthly figures: January has 11, February has 6, March has 15, April has 9, May has 13, and June has 8 television sets repaired.

Step 2: Choose a Symbol for the Pictogram

Select a symbol to represent a certain number of television sets. For this example, let's use a small icon of a TV set to represent 2 television sets repaired. This choice is a balance between size and simplicity for easy visualization.

Step 3: Calculate the Number of Symbols per Month

Divide the number of television sets repaired each month by the amount each symbol represents, which is 2. For example, in January, 11 sets are repaired, so 11 ÷ 2 = 5.5 (round down to 5 symbols, plus a half symbol for clarity). Repeat this for each month.

Step 4: Create the Pictogram

Draw the pictogram using the calculated number of symbols per month. For January, draw 5 full symbols and 1 half symbol; for February, draw 3 full symbols; for March, draw 7 full symbols and 1 half symbol; for April, draw 4 full symbols and 1 half symbol; for May, draw 6 full symbols and 1 half symbol, and for June, draw 4 full symbols.

Step 5: Verify the Representation

Carefully check the pictogram to ensure that each month's data is accurately represented by the symbols. Each symbol stands for 2 sets, and half symbols represent an additional single unit where needed.

Key Concepts

Pictogram

A pictogram is a simple way to display data using pictures or symbols to represent numerical values. It is an effective tool for illustrating quantitative differences in a visually appealing manner. Imagine a bar chart that uses images instead of bars. Each symbol or picture in a pictogram represents a set number of items or units. For instance, if we use a small icon of a TV to represent two repaired television sets, we can easily translate monthly data into icons or symbols.
To create a pictogram:

• Select a symbol for representation; this could be anything relevant to the data, such as a TV symbol for televisions repaired.
• Decide how many units each symbol will represent; in our case, each TV icon stands for two television sets.
• Represent your data with the appropriate number of symbols and, if necessary, adjust for partial numbers with half symbols or other methods.

This visualization method makes it easier for readers to quickly grasp the summarized data without sifting through numerical details.

Numerical Data Interpretation

Numerical data interpretation involves understanding and analyzing quantitative information. It is about extracting meaning from numbers and finding patterns or trends within them. Consider the example of the technician who repaired varying numbers of TVs over a six-month period. By interpreting this numerical data, one can identify which months had higher or lower repair activity.
Key steps in interpreting numerical data include:

• Looking at the raw numbers to understand the differences and patterns (e.g., more TVs were repaired in March, fewer in February).
• Calculating averages, totals, or differences to further understand these patterns.
• Using visual aids like pictograms to better display and interpret these patterns for easier understanding.

Effective numerical data interpretation helps us make informed decisions and draws attention to key insights from what might initially appear as raw numbers.

Symbolic Representation

Symbolic representation is a technique used to convey complex data through symbols or icons, making it easier for the human brain to process and understand. In data visualization, using symbolic representation like a TV icon effectively condenses lots of information into a simple and easily digestible format.
Choosing the right symbol is important because it creates an immediate connection to the data it represents.

• Symbols should be clear and consistent; using different shapes or sizes for a symbol could confuse the viewer.
• The selected symbol should have intuitive meaning relevant to the data. This enhances understanding without needing further explanation.
• Symbols can also incorporate variations like half symbols to depict smaller quantities, which provides greater accuracy in representation.

By using the power of symbolic representation, complex numerical data transforms into an accessible format for a wide audience, facilitating quicker insights and comprehension.