Box-and-whisker plots, also known as box plots, are a visual representation of data distribution. They offer a concise summary of a dataset, highlighting key statistics like the median, quartiles, and outliers. The plot itself is comprised of a box with lines extending from either side, known as whiskers....
Interpreting the Box-and-Whisker Plot
To answer the question, we need to understand the key elements of a box-and-whisker plot:
- Median: The line in the middle of the box represents the median. This is the midpoint of the data, meaning half the values are above and half are below.
- Quartiles: The box itself represents the middle 50% of the data. The left edge of the box is the first quartile (Q1), and the right edge is the third quartile (Q3). This means 25% of the data is below Q1 and 25% is above Q3.
- Whiskers: The lines extending from the box are the whiskers. They usually encompass the remaining 50% of the data, with the exception of outliers.
- Outliers: These are data points that lie significantly far away from the other data points. They are represented by individual points on the plot.
Calculating the Percentage of Data Values
Given that the question asks about data values between 45 and 75, we need to identify these values on the box-and-whisker plot. Let's consider the following possibilities:
- Scenario 1: If 45 falls within the box (Q1-Q3 range) and 75 falls within the box or on the upper whisker, then the percentage of data between these values would be at least 50% (since the box represents the middle 50% of the data).
- Scenario 2: If 45 falls below Q1 and 75 falls within the box or on the upper whisker, the percentage would be greater than 50% (since we're including data below Q1).
- Scenario 3: If both 45 and 75 fall outside the box and on the whiskers, the percentage would be less than 50% (since we're only considering data within the whiskers).
Example
Let's assume the box-and-whisker plot has the following characteristics:
- Q1 = 40
- Q3 = 70
- Lower Whisker = 30
- Upper Whisker = 80
In this case, 45 falls within the box (Q1-Q3) and 75 falls on the upper whisker. Therefore, the percentage of data values between 45 and 75 would be at least 50% (and likely more, since we're including the data on the upper whisker).
Conclusion
To accurately determine the percentage of data values between 45 and 75, we need to have the actual box-and-whisker plot. However, by understanding the interpretation of a box-and-whisker plot, we can estimate the percentage based on the position of 45 and 75 relative to the box, whiskers, and outliers.