Question

Snow Goose Nests. In the article "Trophic Interaction Cycles in Tundra Ecosystems and the Impact of Climate Change" (BioScience, Vol. 55, No. 4, pp. 311-321), R. Ims and E. Fuglei provided an overview of animal species in the northern tundra. One threat to the snow goose in arctic Canada is the lemming. Snowy owls act as protection to the snow goose breeding grounds. For two years that are 3 years apart, the following graphs give relative frequency histograms of the distances, in meters, of snow goose nests to the nearest snowy owl nest.

For each histogram do the following:

(a) Identify the shape of the distribution with regard to modality.

(b) Identify the shape of the distribution with regard to symmetry (non-symmetry).

(c) If the distribution is unimodal and non-symmetric, classify it as either right-skewed or left-skewed.

(d) Compare the two distributions.

Short answer

Ans:

(a) From the year 1 histogram, it is clear that there is a high rate. Therefore, $1-year$distribution is rare.

From the 2nd year histogram, it is clear that there is a single high number. Therefore, $2-year$distribution is rare.

(b) From the year 1 histogram, it is clear that distribution is uneven (non-symmetric).

From the 2nd year histogram, it is clear that the distribution is uneven (non-symmetric).

(c) From the year 1 histogram, it is clear that the distances are directed to the right tail. Therefore, it is right-skewed or well mixed.

From the 2nd year histogram, it is clear that the distance spreads to the right tail. Therefore, it is right-skewed or well distorted.

(d) The $1-year$ histogram has a long tail compared to year 2. Therefore, the $1-year$ difference is more than the 2nd year. In addition, the distribution center is not the same.

Step-by-step solution

Step 1, Given information.

given,

R. Ims and E. Fuglei provided an overview of animal species in the northern tundra. One threat to the snow goose in arctic Canada is the lemming. Snowy owls act as protection to the snow goose breeding grounds.

Step 2. (a)  Identify the shape of the distribution with regard to modality. 

From the year 1 histogram, it is clear that there is a high rate. Therefore, $1-year$ distribution is rare.

From the 2nd year histogram, it is clear that there is a single high number. Therefore, $2-year$ distribution is rare.

Step 3. (b)  Identify the shape of the distribution with regard to symmetry (non-symmetry). 

From the year 1 histogram, it is clear that distribution is uneven (non-symmetric).

From the 2nd year histogram, it is clear that the distribution is uneven (non-symmetric).

Step 4. (c) Classify each histogram as the left or right-skewed.

From the year 1 histogram, it is clear that the distances are directed to the right tail. Therefore, it is right-skewed or well mixed.

From the 2nd year histogram, it is clear that the distance spreads to the right tail. Therefore, it is right-skewed or well distorted.

Step 5. (d)  Comparison,

The 1-year histogram has a long tail compared to year 2. Therefore, the 1 year difference is more than the 2nd year. In addition, the distribution center is not the same.