ECO-2100 Lecture Notes - Lecture 3: Skewness, Frequency Distribution, Unimodality
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Eco 2100 Chapter Three notes
•A histogram is a graphical representation of a frequency distribution.
•The Y-axis of a histogram shows the frequency or percentage (relative frequency) of each bin
Shape:
Modal Class: a histogram bar that is higher than those on either side
Unimodal, bimodal, trimodal, multimodal
Modal classes may be artifacts of the way bin limits are chosen.!
Skewness: the direction of the longer tail of a histogram.
Left skewed - (negatively skewed) a longer left tail
Right skewed - (positively skewed) a longer right tail
Symmetric - both tail areas are the same
Two ways to determine the skewness of the distribution of all data values in a sample
One: plot a histogram
Two: compare the mean, median, and mode
Mode>Median>Mean - skewed left (Mode is largest)
Mean=Median=Mode - symmetric
Mode<Median<Mean - skewed right (Mean is largest)
Chapter Four Notes
Mean:
•The mean is the balancing point
•In Excel, use the function AVERAGE(Data)
Median:
•The median is the midpoint of a sorted sample data.
•If n (sample size) is odd, the median is the middle observation in a sorted data array.
•If n is even, the median is the average of the middle two observations in a sorted data array
•In Excel, use the function MEDIAN(Data)
•Median vs. Mean
•Median is very stable compared to mean
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