2,2.5,3,3.5,4
Analyze Data Shape and Context Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the question.
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 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.
IQR, 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 skewed to the right.
Range, the shape of the distribution is skewed to the right.,4.5,5,5.5,6,6.5,7,7.5,8,8.5,9,9.5
IQR; the shape of the distribution is skewed to the right.
why
The IQR (interquartile range) is a measure of variability that represents the spread of the middle 50% of the data. It is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1).
In the given context, the box plot suggests that the distribution is skewed to the right. This means that there are more data points on the lower end and fewer data points on the higher end of the distribution. The IQR is better suited to represent this type of shape because it focuses on the middle portion of the data, which is where the majority of the values are concentrated. On the other hand, the range (the difference between the maximum and minimum values) would include the extreme values on the higher end, which may not accurately represent the shape of the distribution.