17. Truffles are a great delicacy, sending thousands of mushroom hunters into th

Question

17. Truffles are a great delicacy, sending thousands of mushroom hunters into the forest each fall to find them. A set of plots of equal size in an old-growth forest in Northern California was surveyed to count the number of truffles (Waters et al. 1997). The resulting distribution is pre- sented in the following table. Are truffles ran domly located around the forest? If not, are they clumped or dispersed? How can you tell? (The mean number of truffles per plot, calculated from these data, is 0.60.) Number of truffles per plot Frequency 203 39 18 13 15 > 3

Explanation / Answer

First we will calculate the variance of truffles per plot.

Variance = Sum of (X-0.6)2f / Sum of frequency

= 362.88 /288 = 1.26

Variance/Mean = 1.26 / 0.6 = 2.1 which is greater than 1.

As, Variance/Mean ratio is significantly greater than 1, the population is found to be clumped distribution.

Number of tuffles per plot (X) Frequency (f) (X-0.6) (X-0.6)2 (X-0.6)2f 0 203 -0.6 0.36 73.08 1 39 0.4 0.16 6.24 2 18 1.4 1.96 35.28 3 13 2.4 5.76 74.88 4 (Assumed) 15 3.4 11.56 173.40 Total 288 362.88

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