which statement describes box and whisker plots
A box and whisker plot, also known as a box plot, is a graphical representation of a distribution of a dataset. It provides a visual summary of the data's minimum, first quartile, median, third quartile, and maximum values, as well as any potential outliers.
To create a box and whisker plot, follow these steps:
1. Sort the dataset in ascending order.
2. Find the minimum value, which is the smallest value in the dataset.
3. Find the maximum value, which is the largest value in the dataset.
4. Calculate the median, which is the middle value of the dataset when it is sorted. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.
5. Determine the first quartile, which is the median of the lower half of the dataset. It represents the value below which 25% of the data falls.
6. Determine the third quartile, which is the median of the upper half of the dataset. It represents the value below which 75% of the data falls.
7. Calculate the Interquartile Range (IQR), which is the difference between the third quartile and the first quartile.
8. Identify any potential outliers, which are values that are significantly smaller or larger than the rest of the dataset.
Once you have gathered this information, you can construct the box and whisker plot:
1. Draw a number line that represents the range of the dataset, from the minimum value to the maximum value.
2. Place a rectangular box on the number line, with its lower edge at the first quartile and its upper edge at the third quartile. This box represents the middle 50% of the data.
3. Draw a line segment within the box at the median.
4. Add "whiskers" to the plot by drawing line segments from the ends of the box to the minimum and maximum values, respectively.
5. Optional: Mark any outliers as individual data points or asterisks outside the whiskers.
In summary, a box and whisker plot provides a visual summary of the central tendency, spread, and presence of outliers in a dataset. It is created by calculating specific statistical values and representing them graphically.