2.2 Histograms, Frequency Polygons, and Time Series Graphs
recommended:
Chapter 2 Practice (pp. 108-111): 12-22
Chapter 2 Homework (pp. 117-119): 3-8
histograms are a common graphical representation technique for relatively large
data sets, displaying frequency, or relative frequency, of data values
relatively frequency can also be referred to as percent
frequency, or probability
the horizontal axis of a histogram is divided into classes and the
vertical axis represents frequency, or relative frequency, of the classes
we use several conventions for choosing the number of classes, the
starting and ending points of the classes, and the class widths
frequency polygons use straight lines to connect the points that consist of
the midpoints of the classes and the frequency of the classes, connect to classes
with \( 0 \) frequencies before and after the first and last classes
time series graphs use straight lines to connect points that pair data values
with dates or times
2.3 Measures of the Location of the Data
recommended:
Chapter 2 Practice (pp. 111-112): 23-39
Chapter 2 Homework (pp. 119-120): 9-12
we can divide our data sets with measurements called percentiles and
quartiles
quartiles divide the data set (roughly) into quarters
first quartile, \( Q_{1} \), first quarter of valuees
second quartile, or median, \( M \), first half of valuees
third quartile, \( Q_{3} \), first three quarters of valuees
percentiles divide the data set (roughly) into hundredths
the quartile and percentile values are not necessarily values in
the data set
interquartile range (\( IQR \)) is defined to be the difference between the
\( Q_{3} \) and \( Q_{1} \): \( IQR=Q_{3}-Q_{1}\)
values lower than \( Q_{1}-1.5*IQR \) or above \( Q_{3}+1.5*IQR \) are potential
outliers
2.4 Box Plots
recommended:
Chapter 2 Practice (p. 112): 40-41
Chapter 2 Homework (pp. 120-122): 13-17
box plots - a typewriter-based shorthand for displaying a data set in terms of
the quartiles and the outliers
sometimes called a "box-and-whiskers" plot
sometimes enhanced to show outlier boundaries and outliers