1. Higher National Certificate in Engineering
Unit 36 – LO4.2
Recording Information on Variation

2. Learning Outcome 4.2
Record information on variation from a process.

3. Summary of Recording Methods
Name
Purpose
Application
Interpretation
Ease of Use
Tally
Provides a quick tally of total quantity and by class interval. Provides visual idea of the distribution shape
Used to count defect quantity by type, class and / or category
Tally mark concentration and spread roughly indicate distribution shape. Tally mark of five are crossed out as a group for easy counting. Isolated groups of tally marks indicate uneven distribution
Very easy to create and interpret

4. Summary of Recording Methods
Name
Purpose
Application
Interpretation
Ease of Use
Frequency distribution
Provides a view of numerical data about location and spread
Especially if tally column cells have a large number of marks
Concentration of data is seen as a peak and spread of the data is demonstrated by the width of the curve. Thinner distribution indicates less variation. Distribution can be uni-modal (with one peak) bimodal (two peaks) or multimodal (multiple peaks) indicating a mixture of populations. Distribution with no peak and flat curve indicates rectangular distribution
Not easy to create but easier to interpret

5. Summary of Recording Methods
Name
Purpose
Application
Interpretation
Ease of Use
Stem-and leaf plot
Provides numerical data information about the contents of the cells in a frequency distribution
Useful to quickly identify any repetitive data within the class interval
If data values within cells are not fairly evenly distributed, measurement errors or other anomalous conditions may be present
Easy to create but difficult to interpret

6. Summary of Recording Methods
Name
Purpose
Application
Interpretation
Ease of Use
Box-and whisker plot
Provides a pictorial view of minimum, maximum, median and interquartile range in one graph
Provides more information than distribution plot but easier to interpret. Outliners are easily identified on the graph
If the location of the centre line of the box is right in the middle, the data may be normally distributed. If moved to one of the sides, may be skewed. The data points outside the whiskers indicate outliners. Unequal whiskers indicate skewness of the distribution.
Easy to create and interpret

7. Summary of Recording Methods
Name
Purpose
Application
Interpretation
Ease of Use
Scatter diagrams
Detects possible correlation or association between two variables or cause and effect
Used for root cause analysis, estimation of correlation coefficient, making prediction using a regression line fitted to the data
To estimate correlation the relationship has to be linear. Nonlinear relationship may also exist between variables. If plotted data flow upwards left to right, the relationship is positively correlated. If the plotted data flow downward from left to right the relationship is negatively correlated. If data are spread about the centre with no inclination to right or left, there may not be any correlation
Easy to create and intepret

8. Summary of Recording Methods
Name
Purpose
Application
Interpretation
Ease of Use
Run chart
Provides a visual indicator of any non-random patterns
Used when real-time feedback is required for variables data
Patterns like cluster, mixture, trend and oscillation are spotted based on the number of runs above and below mean or median. P value identifies the statistical variance of a non-random pattern. P value less than 0.05 identifies a stronger significance.
Easy to create and interpret

9. Stem-and-leaf plot
A stem-and-leaf plot is constructed much like a tally column except that the last digit of the data is recorded instead of the tally mark. This plot is often used when data are grouped.
Consider the following…milliwatt power is recorded from a transmission at periodic time intervals….
10.3, 11.4, 10.9, 9.7, 10.4, 10.6, 10.0, 10.8, 11.1, 11.9, 10.9, 10.8, 11.7, 12.3, 10.6, 12.2, 11.6, 11.2, 10.7, 11.4

10. Stem-and-leaf plot
A histogram for this data would be something like…

11. Stem-and-leaf plot N = 20 Leaf unit 0.1 Freq Stem Leaf 1 9 7 4 10 034
(7) 11
1244 5
679 2 12 23

12. Box plot
The box plot (also called box-and-whisker plot) was developed by Professor John Tukey of Princeton University, used high and low values of the data as well as quartiles.

13. Box plot
Outliner – an unusually large or small observation. Values beyond the whiskers are outliners *
The upper whisker extends to the highest value within the upper limit. Upper limit = Q (Q3-Q1)
The top of the box is the third quartile (Q3). 75% of the data vales are less than or equal to this value
The median (middle) value of the data. Half of the observations are less than or equal to it
The bottom of the box is the third quartile (Q1). 25% of the data vales are less than or equal to this value
The lower whisker extends to the lowest value within the lower limit.

14. Box plot
Consider the following data collected from tests undertaken on the strength of adhesive bonds…
8.250, 8.085, 8.795, 9.565, , 9.180, 9.950, 9.630, 8.150
Arranging in ascending order…
8.085, 8.150, 8.250, 8.795, 9.180, 9.565, 9.630, 9.950,
median = 9.180, Q1 = 8.20 Q3 = 9.97

15. Box plot 12 11 10 . 9 8

16. Box plot
Approximately symmetric
Increased Variability
Left Skewed

17. Period Box plot *
10.0
9.5 * *
9.0 2 3 1
Period