Box and Whisker Plots
What do the "whiskers" in a box and whisker plot represent?
The "whiskers" represent the minimum and maximum values of the data set
What is the mean of the numbers 2, 4, 6, and 8?
The mean is 5.
What is the median of the numbers 3, 5, 7, and 9?
What is the mode of the numbers 1, 2, 2, 3, 4?
The mode is 2.
What is the range of the numbers 5, 10, 15, and 20?
The range is 15.
How do you determine the median in a box and whisker plot?
If the mean of five numbers is 10, what is the total sum of those numbers?
The total sum of those numbers is 50.
How do you find the median in a set with an even number of values?
You find the median by averaging the two middle numbers.
Can a data set have more than one mode? Give an example.
Yes, it can. Example: In the set {1, 1, 2}, the mode is 1, but it can also have 2 as a mode if repeated.
How do you calculate the range of a data set?
The range is calculated by subtracting the minimum value from the maximum value
What is the purpose of the box in a box and whisker plot?
How does adding a new number to a set affect the mean?
Adding a new number will change the mean depending on whether the new number is greater or less than the current mean.
If the numbers are 1, 2, 3, 4, 5, and 6, what is the median?
The median is 3.5.
If all numbers in a data set occur only once, what is the mode?
The mode is undefined or there is no mode.
If the range of a set is 30 and the minimum is 10, what is the maximum?
The maximum is 40 (30 + 10).
How many quartiles are represented in a box and whisker plot?
There are four quartiles represented in a box and whisker plot.
What happens to the mean if the largest number in a set is removed?
The mean will generally decrease if the largest number is removed, as the total sum will decrease.
Explain why the median is often preferred over the mean in data sets with outliers.
The median is less affected by outliers, providing a better measure of center in skewed distributions.
How does the mode differ from the mean and median?
The mode is the most frequent value, while the mean is the average, and the median is the middle value.
Explain why the range might not fully represent the spread of a data set.
The range does not account for the distribution of values within the set.
If the minimum value is 2, the first quartile is 5, the median is 7, the third quartile is 10, and the maximum is 15, what does this tell you about the data distribution?
This tells you that the data is spread from 2 to 15, with the majority of values falling between 5 and 10 (the quartiles).
If the mean of a data set is 12 and one number is increased to 20, what will happen to the mean?
The mean will increase because the total sum increases with the new number, thus raising the average.
If the median of a set is 15 and one number is changed to 25, could the median increase? Why or why not?
Yes, the median could increase, depending on how the change affects the middle value of the set.
In the set {1, 1, 2, 2, 3, 4, 4, 5}, what is the mode and why?
The mode is 1, 2, and 4 (bimodal), as they appear most frequently.
If two data sets have the same range, can they have different means? Explain your reasoning.
Yes, they can have different means because the values can be spread differently within the same range.