## Understanding Histograms |

A histogram is little more than a bar chart of frequency distribution, organizing a group of data points into specified ranges. It condenses a data series into an easily interpreted visual, which while convenient can also lead to an oversimplified interpretation of the data. At a minimum, most fiber analysis histograms report the following information: - Average Fiber Diameter (AFD)
- Standard Deviation (SD)
- Coefficient of Variation (CV)
- Percent of Fibers Over 30 Microns (%> 30 μ)
Most of these terms will be recognized from a basic statistics class, and in fact a fiber histogram does represent a statistical analysis of a range of individual fibers. No animal has a uniform fleece, and no fleece sample is uniform either. Average Fiber Diameter is the arithmetic mean of all the individual fibers in the sample. By itself it is a relatively meaningless figure.
This is a histogram of a sample taken from a Shetland Sheep, with an average fiber diameter of 25.4 μ The vertical bars in the chart represent the actual measurement in microns (on the horizontal axis) and the relative number of fibers of each micron (vertical axis). The width of the bars demonstrate that individual fibers ranged from well below 20 μ to well over 40 μ. The "average" tells us very little about the overall quality.
This histogram, from a huacaya alpaca, reports an average fiber diameter of 23.8 μ, not a whole lot finer (1.6 μ) than the previous sample. The histogram provides visual evidence that the fiber sample was much more uniform, in spite of the similar average. The difference in these two fiber samples is captured in the Standard Deviation. In simples terms, 95% of the sample will lie within two standard deviations of the mean, or average. For the Shetland sample, this means that a significant portion of the sample ranges as high as 42 μ, or nearly double the average. The alpaca sample, on the other hand, computes out to 95% of the fiber being 34.4 μ or less. The histogram does a nice job of displaying the uniformity of the fiber by the grouping of the vertical bars, and the computed SD bears out the accuracy of the visual display. In general, the narrower the range of vertical bars on the horizontal axis, the more uniform the fleece. The Coefficient of Variation is a dimensionless number, or a number without any physical units. It represents the SD divided by the AFD and multiplied by 100 in order to be represented as a percentage. In everyday terms we might consider the statement, "Out of every 10 apples I collect, one is rotten." So, 1/10 = 0.01 X 100 = 10%. Using the above examples, the shetland shows a CV of 32.8% while the alpaca shows a CV 22.3%. The lower CV on the alpaca reflects a more uniform fleece, given that the AFD is similar on the two. Care must be taken, since the CV is extremely sensitive to changes in the AFD, particularly as the AFD drops. The percent of fibers over 30 μ provides a rough assessment of the subjective feel of the fiber, since it is generally accepted in fiber industries that anything over that figure will feel rough or scratchy. Again, using the bove examples, it would be safe to conclude that both would feel too scratchy for next to skin use. The shetland sample has over 25% of its fibers over 30 μ, which would classify it as a coarse fiber if it were hand graded, even though it has a relatively low average. This sample, again from an alpaca, illustrates a much finer and uniform fleece than the above two:
The AFD, SD and fibers over 30 μ are all favorable in this sample and demonstrate a fleece that is probably suitable for next to skin wear. |