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Solution to Problem 1:
Displaying Quantitative Data
To transfer the data in the Table of
Prices of Books Sold via an Amazon.com Associate in December 2005,
found on the web page
Statistics101DisplayingQuantitativeData to a Minitab
worksheet, we first highlight all of the entries in the first column
of the table.
Next we right click the highlighted
column to obtain a menu.
We click "Copy." As the table column has
a title and 174 entries, in Minitab's worksheet we highlight all of
the cells under C1 down to row 174. We have:
We right click the highlighted column in
the worksheet to obtain a menu.
We click "Paste Cells" in the menu to
obtain a dialog box with two radio buttons. We click that radio
button next to "Paste as a single column" and click the OK
button to obtain:
By following the same procedure for
the second column, we have both of the table columns transferred to
a Minitab worksheet.
With data transferred, we follow the
procedure set forth in
Dot Plot
Construction Using Minitab Release 13
to obtain the dot plot for Problem 1.
To obtain the leaf-and-stem display
for Problem 1, we follow the procedure set forth in
Stem-and-Leaf
Construction Using Minitab Release 13.
Note that because of the heavy
concentration of prices between $10.00 and $20.00 and the wide range
of prices (from $0.49 to $127.50), the stem-and-leaf display comes
far short of depicting all of the data. Nonetheless, the middle-two
data value entries are ascertainable, to the nearest dollar; the
first of which is (116-(38-20))/2 = 49 (or, alternatively, 174/2 -
38 = 49) leafs to the right of stem 1.
To construct a frequency histogram
with 10 intervals and with x-axis values at the midpoints of the
intervals, we follow the procedure found on
Histogram
Construction Using Minitab Release 13, save that in the
Histogram Options dialog box, we make the following selections:
In the "Midpoint/cutpoint positions"
box, 6.5 specifies the first midpoint, 123.5 specifies the last
midpoint, and 13 specifies the distance between midpoints (or
equivalently, the width of each bar of the histogram). These values
follow quickly from the following observations: (a) The price of the
least expensive book is a bit more than $0 and the price of the most
expensive book is a bit less than $130. (b) This gives us a range of
$130 - $0 = $130. (c) If there are to be ten intervals, each must
have a width of 130/10 = 13. (d) As we have required x-axis values
to be the midpoints of the bar intervals, the midpoint of the first
interval is 13/2 = 6.5 and the midpoint of the last interval is
130 - 6.5 = 123.5.
By clicking the OK button in this
dialog box and by following the remaining steps found on
Histogram
Construction Using Minitab Release 13, we have the following
frequency histogram.
Note that the label of the vertical
scale has been changed from Frequency to Unit Sales, as this is the
commonly used business term for this type of frequency.
The four relative frequency histograms
with 5, 10, 13, and 26 intervals and with x-axis values at the end
points of the intervals follow rather straight forwardly. We provide the Histogram
Options dialog box for the first.
The four relative frequency histograms
appear below.
The cumulative relative frequency
histogram with 26 intervals and with x-axis values at the end points
of the intervals (to the extent that they are shown) appears below.
Note that with a larger number of
intervals, the histogram of a larger data set has a more
curved appearance.
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Statistics
101
