Based on the given data set, the range of sizes is 64-82 cm.
Dinosaur tracks have a mean length that fits other known dinosaur tracks, and the smallest and largest lengths also conform to previously interpreted tracks, but the variation of the data is otherwise not well defined. A well-known and useful measurement for variation is standard deviation, which describes the spread of data around a mean. Standard deviation is the positive square root of another statistical measurement called variance. Standard deviation, which is easily calculated by popular spreadsheet programs, can be applied to a normally distributed sample, which is described by a bell-shaped curve. One standard deviation represents 68% of all measurements on both sides of the mean; two standard deviations represent 95% and three standard deviations represent 99% (Fig. 2.7). Many sets of data from the natural world are not normally distributed, which means that the median (middle value of the data set) will not be in the exact peak of the distribution, making it a skewed distribution. Likewise, many measurements of dinosaurs, such as femur lengths and widths, track lengths, or egg volumes, have skewed distributions, which may reflect the original life distribution or may be artifacts of the sampling and fossil preservation (Chapter 7). With our given
Of course, calculating an average and range is not the end of describing a set of measurements.
FIGURE 2.7 Diagrams showing how quantitative data can be summarized into histograms with curves approximating the distribution of the values. (Left) Normal distribution. (Right) Skewed distribution. The horizontal axis
(abscissa) is in order of increasing value, whereas the vertical axis (ordinate) is in number of observations or data points.
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