Data Storytelling
A histogram shows two peaks of roughly equal height. What does this suggest?
The data may be bimodal, indicating two subpopulations
What display is best for small datasets (n ≤ 20)?
Dot plot or stem-and-leaf plot.
Two boxplots show different medians but similar spreads. What does this mean?
The groups differ in central tendency but have similar variability
In a histogram, if mean > median, the distribution is likely …
Right-skewed.
A quality engineer wants a quick measure of variability for n=5 samples. Which statistic is used?
Range
A boxplot shows one plant’s quality index much more variable than another. What does this imply
That plant’s process is less consistent and may need improvement
What display best compares multiple groups’ spreads and medians?
Boxplots.
If Plant A’s IQR is smaller than Plant B’s, what does that tell us?
Plant A’s process is more consistent
In a boxplot, a whisker is much longer on the left. What does this imply?
Left-skewed distribution.
If variability is high, what is the risk in a manufacturing setting?
Inconsistent product quality
A stem-and-leaf plot shows most values tightly clustered with one extreme outlier. What conclusion can be drawn?
The outlier may distort measures of central tendency; consider median or IQR
Which plot is best to visualize cyclic variation across quarters?
Time series plot
Two histograms have the same mean but different shapes. What does this indicate?
The mean alone is insufficient; distribution shapes differ
Outliers appear as isolated points beyond whiskers. Why are they important?
They may indicate unusual variation or data entry errors
Boxplots of tensile strength show overlapping medians but different IQRs. What decision can be made?
Processes have similar averages but different consistencies; choose the more consistent process.
In a scatterplot, points cluster tightly around a line. What does this indicate?
A strong linear relationship between the variables
What visualization should be used to check normality assumption?
Normal probability plot
Two time series plots show similar averages but one has strong seasonal cycles. What does this mean?
Averages are similar, but variability over time differs.
If data are heavily skewed, which measure of center is most reliable?
The median.
A time series shows a sudden drop after 20th observation. What should be done?
Investigate possible process change or fault
A cumulative frequency plot levels off early. What does this mean about the data distribution?
Most data are concentrated in the lower range of values
What display is best for comparing categories ordered by frequency?
Pareto chart
Two scatterplots show equal correlation coefficients, but one is curved. What does this mean?
Correlation does not capture nonlinear relationships
Why is IQR more robust than range?
Because it ignores extreme values and focuses on the middle 50%
A histogram shows extreme outliers in strength data. How should engineers respond?
Check for defective material, measurement errors, or process failure