9.12: Quick Check

Quick Check

1. You have 30 power values at different voltages. Why is a graph more useful than the table for identifying the safe operating voltage?
2. What chart type is correct for a cable tension parameter sweep? What is wrong with using a bar chart?
3. List the five requirements for a professional engineering graph. For each, state what happens if it is missing.
4. A student plots tension vs. angle and sees a curve that drops sharply from 10° to 30° then levels off. What does this shape tell them, and where should they focus safety margin?
5. A power vs. voltage graph has the y-axis starting at 0.22 W with all data between 0.22 W and 0.25 W. What problem does this create? How should it be fixed?
6. Why are logarithmic scales used for frequency response plots in electrical engineering?
7. Plot power vs. voltage for R = 220 Ω and R = 470 Ω on the same graph (1–15 V). Add a dashed line at P = 0.25 W. For each resistor, identify the maximum safe voltage.
8. [Challenger] The engineers omitted flights with no O-ring damage from their charts. What type of misleading visualization error does this represent? How would plotting all flights have changed the picture?
9. You fit a linear trendline to beam deflection vs. load data and the equation shows y = 2.34E-03x. What is wrong with leaving it in this format, and how do you fix it in Excel?
10. A classmate forces a trendline intercept to zero for a dataset where the y-intercept is clearly not zero. What is wrong with this, and when is forcing through zero the correct choice?
11. You are charting the percentage of engineering bachelor's degrees awarded by discipline. A classmate uses an XY scatter plot. What is wrong with that choice and what should be used instead?

Answers - click to expand

1. A graph is more useful because it shows the pattern immediately. With 30 power values, a table requires the reader to scan row by row to find where the power crosses the safe limit. A graph can show the curve and the rating line at the same time, making the safe operating voltage visible at the intersection.
2. The correct chart type is an XY scatter plot. Cable angle is a continuous numerical input, and tension is a continuous numerical output. An XY scatter plot preserves the numerical spacing between angles.

   A bar chart is wrong because it treats each angle value as a separate category instead of a numerical x-value. That can hide or distort the continuous relationship between angle and tension.

3. Five requirements for a professional engineering graph:
   1. Descriptive title: Without it, the viewer does not know what system or relationship is being shown.
   2. X-axis label with units: Without it, the input variable and its units are unclear.
   3. Y-axis label with units: Without it, the output quantity and its units are unclear.
   4. Appropriate scale: Without it, the graph may exaggerate, compress, or misrepresent the relationship.
   5. Clean formatting: Without it, decorative effects can distract from the data or make the graph harder to read.
4. The curve tells the student that cable tension is highly sensitive to angle at low angles. From 10° to 30°, small changes in angle cause large changes in tension. At higher angles, the curve levels off, meaning the same angle change has a smaller effect.

   The student should focus safety margin on the low-angle region, especially near 10° to 30°. That is where installation error, cable stretch, or geometry changes can produce the largest increase in tension.

5. Starting the y-axis at \(0.22 \text{ W}\) exaggerates the visual difference between values. A small change from \(0.22 \text{ W}\) to \(0.25 \text{ W}\) can appear much larger than it really is.

   For a basic engineering graph, the y-axis should normally start at zero. If a truncated axis is truly necessary, the graph should clearly indicate that the axis is truncated and explain why.

6. Logarithmic scales are used because frequency response data often spans many orders of magnitude, such as \(1 \text{ Hz}\) to \(1 \text{ MHz}\). On a linear scale, the low-frequency region gets compressed near the axis and important behavior can become invisible.

   On a log scale, each factor-of-10 interval takes the same physical space, so the full frequency range can be interpreted more clearly.

7. Use \(P = V^2/R\) for each resistor and plot both curves from \(1\) to \(15 \text{ V}\). Add a horizontal dashed line at \(P = 0.25 \text{ W}\).

   The maximum safe voltage occurs where \(P = 0.25 \text{ W}\), so \(V_\text{max} = \sqrt{PR}\).

   For \(R = 220 \ \Omega\), \(V_\text{max} = \sqrt{(0.25)(220)} = \sqrt{55} \approx 7.42 \text{ V}\).

   For \(R = 470 \ \Omega\), \(V_\text{max} = \sqrt{(0.25)(470)} = \sqrt{117.5} \approx 10.84 \text{ V}\).

   Answer The \(220 \ \Omega\) resistor is safe up to about \(7.4 \text{ V}\). The \(470 \ \Omega\) resistor is safe up to about \(10.8 \text{ V}\), assuming a \(0.25 \text{ W}\) limit.

8. This is a selection bias or omitted-data visualization error. By leaving out flights with no O-ring damage, the chart only showed damaged cases and removed the comparison group needed to understand the relationship between temperature and damage.

   Plotting all flights would have shown both damaged and undamaged launches across the temperature range. That would have made the low-temperature risk pattern more visible and would have helped viewers judge whether cold launches were associated with higher O-ring damage.

9. The equation y = 2.34E-03x is mathematically valid, but it is not reader-friendly for most introductory engineering reports. Many readers will not quickly interpret \(2.34 \times 10^{-3}\), and the slope may be used incorrectly if the units are not clear.

   In Excel, fix it by formatting the trendline label. Right-click the trendline equation, choose the formatting options for the label, and change the number format from scientific notation to a readable decimal format, such as \(y = 0.00234x\). Also make sure the graph or caption identifies the slope units.

10. Forcing the intercept to zero is wrong when the data clearly have a real nonzero intercept. It can distort the slope, hide calibration offsets, and make the model look more theoretically clean than the measurements actually support.

    Forcing through zero is correct when the underlying physics requires zero output at zero input. Examples include ideal Ohm's Law data where \(V = IR\), or beam deflection versus load when zero load should produce zero deflection after proper zeroing. The key rule is that the choice must come from the physical model, not from a desire to make the graph look cleaner.

11. An XY scatter plot is the wrong choice because engineering disciplines are categories, not continuous numerical x-values. A scatter plot implies a quantitative relationship along the x-axis, which does not exist for named disciplines.

    For percentages by discipline, use a pie chart if the goal is to show each discipline's share of the total. Use a column chart if the goal is to compare discipline percentages more directly.