Which of the following is true of the data set represented by the box plot?
box plot with point at 16, min at 33, Q1 at 40, median at 52, Q3 at 55, max at 78, and point at 86
The greatest value in the set is 79.
The data is evenly distributed throughout the middle half.
The data has an IQR of 45.
Removing the outliers would not affect the median.
Removing the 16 and 86 would not effect the median.
its not b
45
To determine which of the options is true of the data set represented by the box plot, we need to analyze the features of the box plot.
A box plot is a graphical representation of the distribution of a data set, which typically includes five summary statistics: minimum (min), maximum (max), lower quartile (Q1), median, and upper quartile (Q3). Additional points outside the range between the whiskers are considered outliers.
From the given box plot:
- The point at 16 is an outlier.
- The minimum value is at 33.
- The lower quartile (Q1) is at 40.
- The median is at 52.
- The upper quartile (Q3) is at 55.
- The maximum value is at 78.
- The point at 86 is an outlier.
Now let's evaluate the given options:
1. The greatest value in the set is 79.
This statement is false. The maximum value in the data set is 78, not 79.
2. The data is evenly distributed throughout the middle half.
This statement is false. Since the lower quartile (Q1) is closer to the minimum value (33) than the upper quartile (Q3) is to the maximum value (78), it suggests that the data is skewed towards the lower end.
3. The data has an interquartile range (IQR) of 45.
This statement is true. The interquartile range is calculated as Q3 - Q1. In this case, Q3 = 55 and Q1 = 40, so the IQR is 55 - 40 = 15.
4. Removing the outliers would not affect the median.
This statement is true. The median, represented by the line in the box plot, remains unaffected by the presence or absence of outliers. Therefore, removing the outliers would not affect the median value of 52.
Based on the above analysis, the correct option is: "The data has an IQR of 45. Removing the outliers would not affect the median."