Analyze Data Shape and Context Quick Check
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Question
Use the image to answer the question.
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 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.
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IQR, the shape of the distribution is skewed to the right.
why did you pick IQR, the shape of the distribution is symmetrical, or close to it.
I apologize for the incorrect response. The correct answer is actually "IQR, the shape of the distribution is skewed to the right." This is because the box in the boxplot is longer on the right side, indicating that the data is spread out more in that direction. This is a characteristic of a right-skewed distribution, and the IQR (interquartile range) is a measure of variability that is less affected by extreme values in the data, making it a better representation of the shape of the distribution in this case. Once again, I apologize for the confusion in my initial response.
Based on the given information, the shape of the distribution can be determined by the measure of variability that best represents it, which is either the range or the IQR (Interquartile Range).
Looking at the box plot, we can see that there is a box divided into two sections, indicating the distribution of the data. The first box extends from 4 to 5.5, and the second box extends from 5.5 to 7. This suggests that the majority of the data is concentrated between these two ranges.
Since both the range and the IQR represent measures of variability, we need to determine which one best represents the shape of the distribution. The range is the difference between the highest and lowest values, while the IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
To determine if the shape of the distribution is symmetrical or skewed, we need to examine the position of the median (Q2) in relation to Q1 and Q3. If the median is closer to Q1 than Q3, the distribution is skewed to the right. If the median is closer to Q3 than Q1, the distribution is skewed to the left. If the median is roughly in the middle of Q1 and Q3, the distribution is symmetrical.
Unfortunately, the image provided in the Quick Check is not accessible, so we cannot directly analyze the location of the median in relation to Q1 and Q3. Therefore, we cannot definitively determine if the shape of the distribution is symmetrical or skewed to the right based on the given information.
However, the given answer choices are:
1. Range; the shape of the distribution is symmetrical, or close to it.
2. IQR, the shape of the distribution is skewed to the right.
3. IQR, the shape of the distribution is symmetrical, or close to it.
4. Range, the shape of the distribution is skewed to the right.
Without further information or the ability to view the image, it is not possible to accurately determine which answer choice is correct.