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
86	53	86	44	32
y: Percentage success for Canada goose nests
63	60	57	30	24

(a) Use a calculator to verify that Σx = 301; Σx² = 20,561; Σy = 234; and Σy² = 12,294.

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?

a. The CV is the ratio of the standard deviation to the mean; the CV for Canada goose nests is higher.

b. 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.    

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

d. The CV is the ratio of the standard deviation to the variance; the CV for Canada goose nests is higher.

e. 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.

g. 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.

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

b. The two groups are equally consistent because the standard deviations are equal.    

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

Answer 1

Solution:-

(a) Σx = 86 + 53 + 86 + 44 + 32 = 301,       Σx2 = 20,561

Σy = 63 + 60 + 57 + 30 + 24 = 234       Σy2 = 12,294.

(b) x = 301/5 = 60/2

s^2 = 610.20

s = 24.70

(c) y = 234/5 = 46.8  

s2 = 335.70  

s = 18.32

(d) X = Coefficient of Variance = σ/µ = 24.7022 / 60.2 = 0.4103 = 41.03%

Y = Coefficient of Variance = σ/µ = 18.3221 / 46.8 = 0.3914 = 39.14%

(e) option c. The CV is the ratio of the standard deviation to the mean; the CV for mallard nests is higher.

=> option C.
------------------------------------

=>X (variance , standard deviation)

Y (variance, standard deviation)