ENGI 3423 - Third Example using MINITAB

In this session we shall use Minitab^® to

open a new (blank) project,
generate values from a probability distribution,
rename a data worksheet,
sort those values into ascending order,
create a stem-and-leaf diagram for these data,
generate summary statistics using Minitab’s defaults for these data,
create a custom histogram for these data.

Open New Project

On the main menu bar, click on "File".
Then click on "New...".

Click on "Minitab Project" and
click on the "OK" button.

A new project will open, with no data in the single worksheet.

New Example

A particular type of lamp filament is known to have a life time that is a random quantity with an exponential distribution. The true mean lifetime of the filaments is known to be 1,000 hours.

Simulate a random sample of 100 such lamp filaments by placing 100 values, drawn randomly from an exponential distribution of mean µ = 1000, in a column in a Minitab worksheet. Generate the following descriptive statistics in Minitab for your sample:

a stem-and-leaf diagram with between seven and twelve stems (leaf unit = 100)
a stem-and-leaf diagram with its leaf unit = 10
a list of descriptive statistics (mean, median, etc.)
a graphical summary
a separate boxplot
an histogram with seven or eight equal-width classes

Generating Random Values

On the main menu bar, click on "Calc".

Then place the cursor over "Random Data".

Then click on "Exponential...".

Click in the box next to "Generate".
Type 100

Click in the box under "Store in column(s):"
(or just press the Tab key).
Type C1

Click in the box next to "Scale:" (or just press the Tab key).
Type 1000.

Leave the "Threshold:" box at its default value of zero.

Click the "OK" button.

Give column C1 a meaningful name.

[Note that your values will not be identical to the values that you see here. Every new generation of random values from a probability distribution will yield a new set of values.]

As the sorted version of these data will appear in column C2,
give that column the name Sorted.

(Don’t forget to save your work often!)

Renaming a Data Sheet

A data sheet can be renamed from the default "Worksheet 1" to a more meaningful name in Minitab’s Project Manager.

One way to access the appropriate part of the Project Manager is to click on the "Show Worksheets Folder" icon.

Another way is to summon the Project Manager to the top of the stack of Windows through the "Window" menu

(or through the equivalent keystroke Ctrl+I)

In the left pane of the Project Manager, right-click on "Worksheet 1".
In the resulting pop-up menu, click on "Rename".

Type the new name for the worksheet and press Enter.

The data sheet has now been renamed.
If you wish, you can save the data sheet separately from the entire Minitab project, from the "File" menu (not shown here).

Sorting Data

Although this step is not required by the problem specification, let us sort the data into ascending order.

In the Data window (not shown here), give an appropriate name, such as "Sorted", to column C2.

On the main menu bar, click on "Data".

Then click on "Sort...".

In the left pane, double-click on the variable name for column C1.
It appears in the top right box, under "Sort column(s):".

Press the Tab key (or use the mouse), to place the cursor in the next box, beside the first "By column:".
In the left pane, double-click on the variable name for column C1.
It appears in the first "By column:" box.

Click on the lowest radio button, "Column(s) of current worksheet:".
Click in the text box below.
In the left pane, double-click on the variable name for column C2.
It appears in the "Column(s) of current worksheet:" box.

Click on the "OK" button.

The sorted version of your data should now be in the second column of your Data window.

[Again, your values won’t match the values that you see here!]

Note that values in the cells of the Data window are rounded to two decimal places. In Minitab 14 the active cell, (row 1 column C2 in the screenshot here), is instead displayed with as many decimal places as will fit in the cell. This feature seems to have been removed in Minitab 15.

Stem-and-Leaf Diagrams

The first stem-and-leaf diagram needs between seven and twelve stems.
The data range lies inside (0, 5500). [Your range may be very different.]
Thus an interval of 500 is ideal and the leaf unit will be 100.

On the main menu bar, click on "Graph".

Then click on "Stem-and-Leaf...".

In this dialog box,

Double click on the variable "Lifetime"
(although "Sorted" works too).
It appears in the top right window.

Click in the box beside "Increment:"
and type 500.

Click on the "OK" button.

The results appear in the session window.

36 values lie in [0, 500).
25 values lie in [500, 1000).
The median lies in [500, 1000).
39 - 21 = 18 values lie in [1000, 1500) and
39 values lie in {1000 or more}.

... and so on, up to ...

1 value lies in [5000, 5500).

Repeating the process,
except for setting
"Increment:" = 100,
yields this output in the Session window.

We can see that the median falls between two classes: 50 observations are at or below the 700’s and the other 50 observations are at or above the 800’s.

Your stem and leaf diagram may look very different.

Minitab 15 retains an inappropriate leaf of 100, while Minitab 13 resets the leaf unit to 10 (so that stems beyond 1000 are double-digits).

Descriptive Statistics

On the main menu bar, click on "Stat".

Then place the cursor over "Basic Statistics".

Then click on "Display Descriptive Statistics...".

In the left pane, double click on either variable name.

It appears in the top right box.

[If you wish to change which items are displayed in the summary statistics, then click on the "Statistics..." button, check the boxes for the desired items and uncheck the other boxes.]

Then click on the "Graphs..." button.

Check the boxes beside
"Histogram of data, with normal curve" and
"Boxplot of data"

Then click on the "OK" button for this window.

Click on the other "OK" button.

These statistics appear in the Session window.

Two other windows have appeared.
The default boxplot shows four outliers (all more than one and a half interquartile ranges above the upper quartile and some of them more than three interquartile ranges above the upper quartile) and a pronounced positive skew:

Again, by double-clicking on the graph, one can modify various features (not demonstrated here).

The default histogram incorporates many of our other results:

The random sample illustrated here came from an exponentially distributed population with a true mean of 1,000 hours. Yet the sample mean is just over 1023 hours. A good batch, perhaps, but not that unlikely to have occurred by chance, (as we shall be able to prove, after we have studied continuous probability distributions).

The distribution of the sample is clearly inconsistent with a normal distribution (the blue bell shaped curve). This is no surprise, as the true exponential distribution is strongly non-normal.

The positive skew is so strong that, although the sample mean lamp filament lifetime is about 1023 hours, half of all of the lamp filaments in this sample burned out in less than 777 hours!

Custom Histogram

We require a true histogram (where the area, not the height, of each bar represents the frequency in that interval), with seven to twelve equal-width bars spanning most of the range (0, 5500).

Bar widths of 500, starting at 0, are ideal.

Rather than starting from scratch, let us modify the default histogram.
Double click on any number by the vertical axis.

On the "Edit Scale" dialog box:

Click on the third tab "Type";

Click the third radio button "Density";

and click the "OK" button.