Stat121 Lesson 7
Which measure is affected by outliers and why?
Mean. Outliers affect the mean because every observation in a data set (including outliers) is used to compute it.
Which measure is best for symmetric data without outliers?
Mean. The mean is preferred over the median because it has nice mathematical properties whenever there are not outliers or strong skewness.
Which measure do you think is the better measure of center for the CEO's annual salaries?
Median. Since the mean is much larger than the median, we suspect that there are a few CEO salaries that are much, much higher than the other CEO's salaries. These really high salaries will inflate the mean, so the median would be a better measure of center.
Which measure is best for strongly skewed data?
Median. Strong skewness affects the mean, so the median is a better measure of center for skewed data.
What is the first step in finding the quartiles?
Order the data
What is the first thing you should do when finding the median?
Order the data. Since the median represents the "middle" of the ordered data, the data must first be ordered when finding the median.
Graphically, what does the median represent?
A value that vertically cuts the area of a histogram in half
True or false: In a boxplot, a box spans from the minimum to the maximum.
False. A box spans from the first quartile to the third quartile in a boxplot.
True or false: If the histogram is symmetric, then the distance between each of the five numbers is the same.
False. For symmetric data, the distance between minimum and the first quartile will be about the same as the distance between the third quartile and the maximum. And the distance between the first quartile and the median and the median and the third quartile will be about the same. But all the distances do not have to be the same for symmetric data.
True or false: Quartiles split the ordered data into five equally sized data sets
False. It splits it into 4.
True or false: the five numbers in the five-number summary are: minimum, 1st quartile, mean, 3rd quartile and maximum
False. The median is the middle value of the five-number summary, not the mean.
True or false: If a histogram is skewed to the right, then the corresponding boxplot will have a long line on the left or lower end.
False. The opposite is true. If a histogram is skewed to the right, then the corresponding boxplot will have a long line on the right as well.
When finding Q1 and Q3, if n is even, what should you do with the median value?
It splits the ordered data in half, but is not one of the data values, so don't do anything with it.
When finding Q1 and Q3, if n is odd, what should you do with the median value?
Leave it out of both the lower half and the upper half of the ordered data.
The five-number summary of test scores in an introductory statistics class is: Min = 23% Q1 = 71% Median = 83%, Q3 = 86% and Max = 100%. What is the shape of the boxplot for these data?
Left skewed
Since the mean is much larger than the median, what shape do you predict that the histogram of the CEO's annual salaries to have?
Skewed. Since the mean is much larger than the median, we suspect that there are a few CEO salaries that are much, much higher than the other CEO's salaries. Thus, the shape of the histogram would be right-skewed.
What does Q3 correspond to?
The "median" of the upper half of the data.
If n is even, what is the median?
The average of the middle two observations of the ordered data
Graphically, what does the mean represent?
The balance point of the data
What does the symbol "n" represent?
The letter "n" represents sample size in statistics.
What does the median represent?
The median is a value that cuts the ordered data in half.
What does the second quartile correspond to?
The median. Since the second quartile splits the data in half, it is the median.
If n is odd, what is the median?
The middle observation of the ordered data
What does "Σ" represent?
The sum of all the numbers following this symbol.
True or false: If a histogram is symmetric, then the corresponding boxplot will also be symmetric.
True
True or false: The unit of measure for the median is the same as the unit of measure of the data.
True
True or false: The entire boxplot spans from the minimum value of a data set to the maximum value.
True.
True or false: The larger the distance between two adjacent numbers in the five-number summary, the more spread out the data in that interval.
True.
True or false: The line drawn in the box of a boxplot indicates the location of the median.
True.
True or false: The longer the boxplot, the more variable the data displayed in the boxplot.
True.
True or false: The unit of measure for the mean is the same as the unit of measure of the data.
True.
Why is the median the preferred measure of center?
When the shape is strongly skewed, the median is the preferred measure of center.
What does Q1 correspond to?
the ''median'' of the lower half of the data. Since Q1 splits the lower half of the data in half, it is the median of the lower half of the data.
What does the symbol "x¯" represent?
the mean of a data set
