The range of a set of data is 15, and the interquartile range of the same set is 12. Which of the following statements is true about the set?
A) The two ranges are close together, so there is probably an outlier in this set
B) The two ranges are close together, so there are probably no outliers in this set
C) The two ranges are far apart, so there is probably an outlier in this set
D) The ranges are far apart, so there are probably no outliers in this set.
I have no idea how to even start to figure this out! Thanks for all the help!
B)The two ranges are close together, so there are probably no outliers in this set.-John McMuffin
Sources: (Many calculators :D)
2 years later he gets the answer😂😂🤣🤣😅😅😄😁😊
To determine which statement is true about the set, we need to understand what the range and interquartile range represent in relation to outliers.
The range of a set is the difference between the maximum and minimum values. In this case, the range is 15, suggesting that there is a considerable spread between the highest and lowest values in the set.
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of the data. It represents the range of the middle 50% of the data. In this case, the IQR is 12, showing that the middle half of the data has a smaller spread compared to the entire range.
Given this information, we can now analyze the statements:
A) The two ranges are close together, so there is probably an outlier in this set.
This statement is incorrect because if the ranges were close together, the difference between the range and IQR would be small, not large.
B) The two ranges are close together, so there are probably no outliers in this set.
This statement is also incorrect, as we have a large difference between the range and IQR.
C) The two ranges are far apart, so there is probably an outlier in this set.
This statement is correct. The fact that the range (15) is greater than the IQR (12) suggests that there are values at the extremes of the set, which could indicate the presence of outliers.
D) The ranges are far apart, so there are probably no outliers in this set.
This statement is incorrect since we determined in option C that there is likely an outlier present in the set.
Therefore, the correct statement would be: C) The two ranges are far apart, so there is probably an outlier in this set.
To determine which statement is true about the set based on the given information, we need to understand what the range and interquartile range represent.
The range is the difference between the highest and lowest values in a set of data. In this case, the range is 15, meaning the highest value minus the lowest value is equal to 15.
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset. It measures the spread or dispersion of the middle 50% of the data. In this case, the IQR is 12, meaning Q3 minus Q1 is equal to 12.
Now let's analyze the given answer choices:
A) The two ranges are close together, so there is probably an outlier in this set.
B) The two ranges are close together, so there are probably no outliers in this set.
C) The two ranges are far apart, so there is probably an outlier in this set.
D) The ranges are far apart, so there are probably no outliers in this set.
Since the range and IQR are both measures of the spread or dispersion of the data, the statement that makes sense is that when the two ranges are close together, there are probably no outliers in the set. Therefore, the correct answer is:
B) The two ranges are close together, so there are probably no outliers in this set.