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
IQR, the shape of the distribution is symmetrical, or close to it.
IQR, 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.
Range, the shape of the distribution is skewed to the right.
Range, the shape of the distribution is skewed to the right.
Range; the shape of the distribution is symmetrical, or close to it.
Range; the shape of the distribution is symmetrical, or close to it.
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IQR, the shape of the distribution is symmetrical, or close to it.
The ages (in years) of 10 randomly selected individuals are 24, 15, 18, 30, 32, 40, 22, 27, 33, and 35. Form a new dataset by replacing the maximum age with 50. Which statement best compares the two datasets?(1 point)
Responses
The range of the original dataset is higher than the range of the new dataset.
The range of the original dataset is higher than the range of the new dataset.
The mean of the new dataset is lower than the mean of the original dataset.
The mean of the new dataset is lower than the mean of the original dataset.
The original dataset is more dispersed than the new dataset.
The original dataset is more dispersed than the new dataset.
The mean of the new dataset is higher than the mean of the original dataset.
The mean of the new dataset is higher than the mean of the original dataset.
The original dataset is more dispersed than the new dataset.
Use the image to answer the question.
Two box plots. One is labeled 'Math Scores' while the other is labeled 'Science Scores.' The plots are placed over a number line that ranges from 0 to 30 in increments of 5. The 5 number labels typical to box plots are available for both. The box plot for math scores shows the following labels: minimum: 5; first quartile: 10; median: 15; third quartile: 20; maximum: 25. The box plot for science scores shows the following labels: minimum: 6; first quartile: 12; median: 16; third quartile: 20; maximum: 24.
Which statement is true about the given datasets?
(1 point)
Responses
The math scores are less spread out than the science scores.
The math scores are less spread out than the science scores.
The range of the science scores is higher than the range of the math scores.
The range of the science scores is higher than the range of the math scores.
The interquartile range (IQR) of the science scores is lower than the IQR of the math scores.
The interquartile range (IQR) of the science scores is lower than the IQR of the math scores.
The median of the math scores is higher than the median of the science scores.
The median of the math scores is higher than the median of the science scores.
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The interquartile range (IQR) of the science scores is lower than the IQR of the math scores.
Based on the given information, the best measure of variability that represents the shape of the distribution is the IQR (Interquartile Range).
To determine which measure of variability, range or IQR (interquartile range), best represents the shape of the distribution, we need to understand the characteristics of each measure.
Range is the simplest measure of variability, calculated by subtracting the minimum value from the maximum value in the dataset. It gives an idea of how spread out the data points are across the entire number line.
IQR, on the other hand, is a robust measure of variability that provides information about the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). The IQR is less sensitive to extreme outliers compared to the range.
Based on the given information of the boxplot, it shows the distribution of the data from 2 to 9.5 on the number line. The box itself is divided into two sections, with the first section extending from 4 to 5.5 and the second section extending from 5.5 to 7.
Since the box represents the middle 50% of the data and spans from 4 to 7, this suggests that the majority of the data falls within this range. Furthermore, the line segments extending from each end of the box, terminating at 2 on the left and terminating at 9.5 on the right, indicate the maximum and minimum values respectively.
Based on these observations, we can conclude that the shape of the distribution is not symmetrical but instead skewed to the right, as indicated by the extended range on the right side. A skewed distribution means that one tail of the distribution is longer or stretched out compared to the other.
Considering the skewed shape of the distribution, the IQR is a better measure of variability to represent the spread of the middle 50% of the data. Therefore, the correct answer is:
IQR, the shape of the distribution is skewed to the right.