Below are boxplots that summarize the weights (in pounds) of large samples from two breeds of dog: the Anatolian Shepherd and the Black Russian Terrier. (a) Compare the distributions of weights for the two dog breeds. (b) This sample of Black Russian Terriers does not contain any outliers. What weights would a Black Russian Terrier have to be to be considered an outlier

The comparison of the distribution of the weights of the two dog breeds are:

The weights that would be considered as outliers for a Black Russian Terriers are weights less than 67.5 pounds or weights greater than 167.5 pounds

From the boxplots, we have the following highlights:

Anatolian Shepherd

- Range = 75 (i.e. 175 - 100)

- Median = 120

- Left skewed, because the data points are concentrated on the right

Black Russian Terrier

- Range = 75 (i.e. 155 - 80)

- Median = 120

- Right skewed, because the data points are concentrated on the left

From the box plot, we have:

The boundaries of the outliers are calculated using:

This gives

Hence, the weights that would be considered as outliers for a Black Russian Terriers are weights less than 67.5 pounds or weights greater than 167.5 pounds

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(a) The median of both plots is same, 120 pounds is the median weight of Anatolian Shepherd and the Black Russian Terrier breed.

The range of both plots is also same that is 75 pounds.

The box plot of Anatolian Shepherd is skewed towards left therefore, it is considered to be positively distributed.

The box plot of Black Russian Terrier is skewed towards right therefore, it is considered to be negatively

(b) Any data point which is greater than 155 or smaller than 80 will be considered an outlier.

Step-by-step explanation:

A box plot is a graph which shows five statistical characteristics of a data set.

1. Maximum value

2. Minimum value

3. Median

4. Upper Interquartile

5. Lower interquartile

(a) Compare the distributions of weights for the two dog breeds

Please refer to the attached diagram of the question.

The median of both plots is same, 120 pounds is the median weight of Anatolian Shepherd and the Black Russian Terrier breed.

The range of Anatolian Shepherd is,

Range = Maximum value - Minimum value

Range = 175 - 100 = 75 pounds

The range of Black Russian Terrier is,

Range = Maximum value - Minimum value

Range = 155 - 80 = 75 pounds

Therefore, the range of both plots is also same that is 75 pounds.

A box-plot is considered to be normally distributed when the median is at the center of upper quartile and lower quartile.

The box plot of Anatolian Shepherd is skewed towards left therefore, it is considered to be positively distributed.

The box plot of Black Russian Terrier is skewed towards right therefore, it is considered to be negatively distributed.

(b) What weights would a Black Russian Terrier have to be to be considered an outlier?

An outlier is a data point in the data set that is very different from the other data points.

In this case, the maximum and minimum values in the Black Russian Terrier box-plot are

Maximum = 155

Minimum = 80

Therefore, any data point which is greater than 155 or smaller than 80 will be considered an outlier.