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Statistics
MINITAB - Lab 7
Box Plots in MINITAB
A boxplot in MINITAB consists of a box, whiskers, and extreme observations.
Left and right (lower
and upper) hinges of
the box
------------------I
+
I------------- **
*
*
-----------+---------+---------+---------+---------+---------+---40
60
80
100
120
140
Whiskers
All extreme observations
are marked with an *
A ‘+’ is drawn in the box at the median. By default, the left hinge of the box is at the first quartile
(Q1) value and the right hinge is at the third quartile (Q3) value. (Here Q1  67 and Q3  87) The
whiskers are the lines that extend from the box to the adjacent values. The adjacent values are
the lowest and highest observations that are still inside the region defined by the following limits:
Lower Limit:
Q1 - 1.5 (Q3 – Q1)
Upper Limit:
Q3 +1.5 (Q3 – Q1)
(Here the upper and lower limits define the region between 37 and 117 approx. Verify these
values for yourself with the formulas. From the boxplot we can see that the end of the lower
whisker is  49, so 49 is the lowest observation in the dataset within the region, similarly 113 is the
highest value in the dataset within the region.)
Extreme observations are points outside of the lower and upper limits and are plotted with
asterisks (*). Note: Minitab does not differentiate between inner and outer fences when plotting
extreme observations. Therefore all extreme observations are plotted with an * and 0 is not used
for the most extreme observations.
1
1.
Open the Minitab worksheet called Downtime.MTW. This found on the online class for this
course.
A manufacturer of minicomputer systems is interested in improving its customer support
services. As a first step, its marketing department has been charged with the responsibility
of summarising the extent of customer problems in terms of system down time. The 40
most recent customers were surveyed to determine the amount of down time (in hours)
they had experienced during the previous month. The data “Customer Number” and “Down
Time” are in C1 and C2 of DOWNTIME.MTW, respectively.
2.
Use Minitab Graph > Character Graphs > Boxplot to construct a boxplot for this data.
Using the boxplot get approximate values for the following:
What is the median down time __________________
What is the interquartile range ___________________
What type of skew (left/right) if any is apparent from the boxplot _______________
3.
Using Minitab calculate the mean, standard deviation and median of the of downtime:
Mean = ________
Standard Deviation = __________ Median = ____________
If we assume that downtime is approximately normally distributed what is the probability of
having a downtime greater that 47 ? _____________________
4.
Use your boxplot to determine which customers are having extreme down times.
Let us imagine that a decision has been made that any extreme downtimes are genuine
outliers (i.e. are values that for some reason do not truly represent the distribution of
downtimes.) Set the downtimes for these customers to missing values by replacing their
downtimes with an *. Now redraw the boxplot and note any changes from last time.
_______________________________________________________________________
_______________________________________________________________________
5.
Calculate the mean standard deviation and median of the amended data (with the outliers
set to missing).
2
Mean = ________
Standard Deviation = __________ Median = ____________
Why is the mean lower now ? _______________________________________________
Why is the standard deviation lower now ? ______________________________________
Why is the median lower now ? _______________________________________________
Do you think the assumption of normality is more reasonable now ? Why ?
_______________________________________________________________________
What is the probability of having a downtime greater than 47 now ? Why has this
probability changed from last time ?
_______________________________________________________________________
_______________________________________________________________________
Using the empirical rule what is the range (in hours of downtime) within which you would
expect to find 68% of your data ?
range from ______________ to _______________.
What percentage of values in the amended data set are outside this range ? _________
ASSIGNMENT:
Part 1:
Open the dataset Variables.MTW again. Generate a boxplot of both VARS1 and VARS2
on the same axes by:
Graph => Boxplot
Click on VARS1 under Y for Graph 1 and VARS2 under Y for Graph 2.
Click on Frame => Multiple Graphs => Overlay graphs on the same page
If your boxplots have colour in the centre box it can be difficult to interpret them. Generate
the graphs again and change this under ‘Edit Attributes’.
3
Compare the two boxplots and comment on the differences:
_______________________________________________________________________
_______________________________________________________________________
______________________________________________________________________
Part 2:
Using the empirical rule calculate the following intervals (in hours of downtime) for the
data with the extreme observations set to missing.
Interval containing approx.
% of data by empirical rule
95%
from ___________ to _______________
99.7%
from ___________ to _______________
What is the lowest standardised score (Z score) it is possible to have with this data set ?
_____________
Can you see any theoretical problem with applying the empirical rule to this set of data ?
_______________________________________________________________________
_______________________________________________________________________
REVISION SUMMARY
After this lab you should be able to :
-
Know how to generate Boxplots in Minitab
-
Understand how to generate a boxplot yourself by hand
-
Understand how to interpret a boxplot, ie get the mean, median, interquartile range and
identify any skew, outliers
-
Know how to spot if assuming a normal distribution is reasonable
-
Generate summary statistics (done before)
-
Calculate a probability assuming a normal distribution (done before)
-
Generate two boxplots on the same page
END
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