Question

For mallard ducks and Canada geese, what percentage of nests are successful (at least one offspring survives)? Studies in Montana, Illinois, Wyoming, Utah, and California give the following percentages of successful nests (Reference: The Wildlife Society Press, Washington, D.C.). x: Percentage success for mallard duck nests 11 23 44 53 65 y: Percentage success for Canada goose nests 39 15 48 15 39 (a) Use a calculator to verify that Σx = 196; Σx2 = 9,620; Σy = 156; and Σy2 = 5,796. Σx Σx2 Σy Σy2 (b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x, the percent of successful mallard nests. (Round your answers to two decimal places.) x s2 s (c) Use the results of part (a) to compute the sample mean, variance, and standard deviation for y, the percent of successful Canada goose nests. (Round your answers to two decimal places.) y s2 s (d) Use the results of parts (b) and (c) to compute the coefficient of variation for successful mallard nests and Canada goose nests. (Round your answers to one decimal place.) x y CV % % Write a brief explanation of the meaning of these numbers. What do these results say about the nesting success rates for mallards compared to Canada geese? The CV is the ratio of the standard deviation to the mean; the CV for Canada goose nests is higher. The CV is the ratio of the standard deviation to the mean; the CV for Canada goose nests is equal to the CV for mallard nests. The CV is the ratio of the standard deviation to the mean; the CV for mallard nests is higher. The CV is the ratio of the standard deviation to the variance; the CV for Canada goose nests is higher. The CV is the ratio of the standard deviation to the variance; the CV for Canada goose nests is equal to the CV for mallard nests. The CV is the ratio of the standard deviation to the variance; the CV for mallard nests is higher. Would you say one group of data is more or less consistent than the other? Explain. The x data group is more consistent because the standard deviation is smaller. The two groups are equally consistent because the standard deviations are equal. The y data group is more consistent because the standard deviation is smaller.

Answer 1

x: Percentage success for mallard duck nests

y: Percentage success for Canada goose nests

a).necessary calculation table for verification:-

11	39	121	1521
23	15	529	225
44	48	1936	2304
53	15	2809	225
65	39	4225	1521

hence, all are verified.

b).table containing the mean:-

necessary calculation table for standard deviation:-

x	y
11	39	795.24	60.84
23	15	262.44	262.44
44	48	23.04	282.24
53	15	190.44	262.44
65	39	665.64	60.84
		sum = 1936.8	sum = 928.8

so, the standard deviation and variance be:-

sample variance ( var(x))		standard deviation()
sample variance ( var(y))		standard deviation()

c). table containing the coefficient of variation:-

	coefficient of variation	interpretation
mallard duck	%	the coefficient of variation shows 56.1% of variability of data in sample of mallard duck in relation to the mean of the population
Canada goose	%	the coefficient of variation shows 48.8% of variability of data in sample of Canada goose in relation to the mean of the population

these results say about the nesting success rates for mallards compared to Canada geese that:-

The CV is the ratio of the standard deviation to the mean; the CV for mallard nests is higher.

the explanation be:-

The y data group is more consistent because the standard deviation is smaller.

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