2.2 organizing quantitative data. data o consider the following data o we would like to compute the...
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2.2Organizing Quantitative
Data
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DataO Consider the following data
O We would like to compute the frequencies and the relative frequencies
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Show the Frequency and Rel. Frequency
Number
Tally Freq. Rel. Freq.
1
2
3
4
5
6
7
8
9
10
11
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HistogramO Discrete quantitative data can be
presented in bar graphs in several of the same ways as qualitative data
O We use the discrete values instead of the category names
O We arrange the values in ascending order
O For discrete data, these are called histograms
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Histograms
OExample of histograms for discrete dataO FrequenciesO Relative frequencies
OUse calculatorO Enter values from table into a listO Plot values and change to
histogram
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Histogram – Discrete Data
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Calculator PracticeO Making a histogram
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ClassesO Continuous data cannot be put directly
into frequency tables since they do not have any obvious categories
O Categories are created using classes, or intervals of numbers
O The continuous data is then put into the classes
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ClassesO For ages of adults, a possible set of
classes is20 – 2930 – 3940 – 4950 – 59
60 and olderO For the class 30 – 39
O 30 is the lower class limitO 39 is the upper class limit
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Class Width● The class width is the difference between
the upper class limit and the lower class limit
● For the class 30 – 39, the class width is40 – 30 = 10
● Why isn’t the class width 39 – 30 = 9? The class 30 – 39 years old actually is 30 years
to 39 years 364 days old … or 30 years to just less than 40 years old
The class width is 10 years, all adults in their 30’s
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Open Ended Classes● All the classes (20 – 29, 30 – 39, 40 –
49, 50 – 59) all have the same widths, except for the last class
● The class “60 and above” is an open-ended class because it has no upper limit
● Classes with no lower limits are also called open-ended classes
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O The classes and the number of values in each can be put into a frequency table
O How many people are between 30 and 39 years old?
Age Number
20 – 29 533
30 – 39 1147
40 – 49 1090
50 – 59 493
60 and older 110
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Histogram – continuous data
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Stem-and-Leaf Plot● A stem-and-leaf plot is a different way to
represent data that is similar to a histogram
● To draw a stem-and-leaf plot, each data value must be broken up into two components The stem consists of all the digits except for
the right most one The leaf consists of the right most digit For the number 173, for example, the stem
would be “17” and the leaf would be “3”
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Stem-and-Leaf Plots● Modifications to stem-and-leaf plots
Sometimes there are too many values with the same stem … we would need to split the stems (such as having 10-14 in one stem and 15-19 in another)
If we wanted to compare two sets of data, we could draw two stem-and-leaf plots using the same stem, with leaves going left (for one set of data) and right (for the other set)
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Create a Stem-and-leaf plot
O Birth DATE for students in this class
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Dot PlotO A dot plot is a graph where a dot is placed
over the observation each time it is observed
O Not extremely useful but help give us a quick view of distribution
O Make a Dot Plot with the Birthday MONTH
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Distribution ShapeO A useful way to describe a variable is by
the shape of its distributionO Some common distribution shapes are
O UniformO Bell-shaped (or normal)O Skewed rightO Skewed left
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UniformOA variable has a uniform distribution
whenO Each of the values tends to occur with
the same frequencyO The histogram looks flat
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Bell-ShapedOA variable has a bell-shaped
distribution whenO Most of the values fall in the middleO The frequencies tail off to the left and to
the rightO It is symmetric
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Skewed RightOA variable has a skewed right
distribution whenO The distribution is not symmetricO The tail to the right is longer than the
tail to the leftO The arrow from the middle to the long tail
points right
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Skewed LeftOA variable has a skewed left
distribution whenO The distribution is not symmetricO The tail to the left is longer than the tail
to the rightO The arrow from the middle to the long tail
points left
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Identify the Shape of the Following
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Time-Series GraphO The following is an example of a
time-series graphO The horizontal axis shows the
passage of time
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