The box plot below summarize the distributions of SAT verbal and math scores among students at an upstate New York high school. 300 400 500 600 700 800 data Whic of the following statements is false? 1. The range of the math scores equals the range of the verbal scores. 2. The highest math score equals the median verbal score. 3. The verbal scores are roughly symmetric, while the math scores are skewed to the right. 4. The interquartile range for the math scores is smaller than the interquartile range for the verbal scores.
We do not have the box plot available.
1 and 2
To answer the question, let's analyze each statement one by one.
1. The range of the math scores equals the range of the verbal scores.
To determine the range, we need the minimum and maximum values of each distribution. However, the given box plot does not provide this information, so we cannot determine if this statement is true or false based on the given data.
2. The highest math score equals the median verbal score.
Again, the box plot does not provide the actual values of the highest math score or the median verbal score. Therefore, we cannot determine if this statement is true or false based on the given data.
3. The verbal scores are roughly symmetric, while the math scores are skewed to the right.
From the box plot, we can infer that the median line of the verbal scores is approximately in the middle of the box, indicating symmetry. However, the right whisker of the math scores is longer than the left whisker, suggesting a right skew. Therefore, statement 3 is true.
4. The interquartile range for the math scores is smaller than the interquartile range for the verbal scores.
The interquartile range (IQR) is represented by the length of the box in the box plot. Comparing the lengths of the boxes for both distributions, it appears that the box for the math scores is smaller than the box for the verbal scores. Therefore, statement 4 is false.
In conclusion, statement 4 is the false statement.
To determine which of the given statements is false, let's analyze each statement:
1. The range of the math scores equals the range of the verbal scores.
To find the range, subtract the minimum value from the maximum value for each set of scores. Given the data provided (300, 400, 500, 600, 700, 800), the range for both math and verbal scores is 800 - 300 = 500. This statement is true.
2. The highest math score equals the median verbal score.
To determine the median, arrange the scores in order and find the middle value. From the given data, we can see that the highest math score is 800, but the median verbal score cannot be determined since the exact values are not given. This statement is inconclusive.
3. The verbal scores are roughly symmetric, while the math scores are skewed to the right.
To determine symmetry and skewness, we need additional information, such as the position of the median within the data set or the relationship between the mean and median. Without this information, we cannot determine the accuracy of this statement.
4. The interquartile range for the math scores is smaller than the interquartile range for the verbal scores.
To find the interquartile range (IQR), subtract the first quartile (Q1) from the third quartile (Q3). Without the exact values for each quartile, we cannot compare the IQRs for math and verbal scores.
Based on the available information, only statement 2 is inconclusive. Therefore, the false statement is not among the given options.