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A number line ranges from 2 to 9.5 in increments of 0.5. A boxplot is placed above the number line. The box is divided into two sections. The first box extends from 4 to 5.5. The second box extends from 5.5 to 7. A line extends from each end of the box, terminating at 2 on the left and terminating at 9.5 on the right.

For the given box plot, which measure of variability—range or IQR—best represents the shape of the distribution?

(1 point)
Responses

Range, the shape of the distribution is skewed to the right.
Range, the shape of the distribution is skewed to the right.

IQR, the shape of the distribution is symmetrical, or close to it.
IQR, the shape of the distribution is symmetrical, or close to it.

Range; the shape of the distribution is symmetrical, or close to it.
Range; the shape of the distribution is symmetrical, or close to it.

IQR, the shape of the distribution is skewed to the right.

1 answer

To determine which measure of variability—range or IQR—best represents the shape of the distribution given the boxplot description, we can analyze the provided information.

  1. Range: The range is the difference between the maximum and minimum values. In this case, the range would be 9.5 (maximum) - 2 (minimum) = 7.5. The range provides an indication of the overall spread of the data but can be influenced by extreme values (outliers).

  2. IQR (Interquartile Range): The IQR measures the spread of the middle 50% of the data, calculated as Q3 - Q1. Based on the boxplot, Q1 is 4 (the lower edge of the first box), and Q3 is 7 (the upper edge of the second box). Therefore, IQR = 7 - 4 = 3. The IQR gives a more robust measure of variability, especially in skewed distributions, as it reduces the influence of outliers.

Now we consider the shape of the distribution:

  • The fact that there is a long whisker extending from the lower end (terminating at 2) and a shorter whisker to the right (terminating at 9.5) suggests that the distribution has a long tail to the left, which indicates it is likely skewed to the right.

Considering both measures of variability and the description of the shape, the best answer would be:

Range, the shape of the distribution is skewed to the right.