Free Lean Six Sigma Green Belt Basic Statistical Tools Questions and Answers — Questions and Answers
Question 1: A team is analyzing the cycle time for a claims process. The data set is highly skewed to the right due to a few complex claims that took an exceptionally long time to resolve. Which measure of central tendency would provide the MOST representative value for a 'typical' claim's cycle time?
- Mode
- Mean
- Median (Correct answer)
- Range
Correct answer: Median
The median is the middle value in a dataset and is resistant to the effects of extreme outliers. The mean (average) would be pulled higher by the few very long cycle times, giving a distorted view of the typical time. The mode is the most frequent value, which may not be representative of the center, and the range is a measure of dispersion, not central tendency.
Question 2: In the context of process improvement, what does a low standard deviation signify?
- The process is not meeting customer specifications.
- The process data points are tightly clustered around the mean. (Correct answer)
- The process has a high degree of special cause variation.
- The process mean is significantly different from the median.
Correct answer: The process data points are tightly clustered around the mean.
Standard deviation is a measure of the dispersion or spread of data. A low standard deviation indicates that the data points tend to be very close to the mean, implying a consistent and predictable process output. A high standard deviation signifies greater variability.
Question 3: A Green Belt wants to create a graphical summary of a large set of continuous data to understand its underlying frequency distribution, central tendency, and shape (e.g., symmetry or skewness). Which tool is MOST appropriate for this purpose?
- Pareto Chart
- Run Chart
- Scatter Plot
- Histogram (Correct answer)
Correct answer: Histogram
A histogram is a bar chart that groups continuous data into bins and displays the frequency of data points in each bin. This visualization is ideal for showing the shape, center, and spread of the data, making it easy to see if the distribution is symmetric, skewed, or has multiple modes.
Question 4: According to the Empirical Rule for a normal distribution, approximately what percentage of data points will fall within two standard deviations of the mean?
- 68%
- 95% (Correct answer)
- 99.7%
- 50%
Correct answer: 95%
The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Question 5: A project team needs to compare the performance distributions of three different production shifts. They want a visual tool that clearly displays the median, quartiles, and any potential outliers for each shift side-by-side. Which statistical tool should they use?
- Run Chart
- Histogram
- Box Plot (Correct answer)
- Scatter Diagram
Correct answer: Box Plot
A Box Plot (or Box-and-Whisker Plot) is specifically designed to display the five-number summary (minimum, first quartile, median, third quartile, and maximum) and identify outliers. It is an excellent tool for comparing the distributions of multiple datasets or categories, such as different production shifts.
Question 6: Which of the following statistics is a measure of dispersion in a dataset?
- The mean
- The median
- The mode
- The range (Correct answer)
Correct answer: The range
Measures of dispersion (or variability) describe the spread of data. The range, which is the difference between the maximum and minimum values, is a simple measure of dispersion. The mean, median, and mode are all measures of central tendency, which describe the center of a dataset.
Free Lean Six Sigma Green Belt Basic Statistical Tools Questions and Answers
A team is analyzing the cycle time for a claims process.
The data set is highly skewed to the right due to a few complex claims that took an exceptionally long time to resolve.
Which measure of central tendency would provide the MOST representative value for a 'typical' claim's cycle time?