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I have a data set that has customerID and daily visits. This dataset records the number of times customers visited the site in a day.

customerID   TotalVisits
 1            6
 2            17
 3            20
 4            25

Just to explore the data further, I tried plotting the TotalVisits values in a box plot. The plot doesn't seem to have a lower whisker. q1=1 and there are no values between q1 and q1-1.5(IQR). The plot has q1, q2 and q3. The minimum value and q1 are the same.

Is this why the boxplot doesn't have the lower whisker? Could you please help me with the interpretation? Is it correct to draw a boxplot without any whiskers?

[I am new to the site and I am not able to post the image.]

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  • $\begingroup$ @Nick I think the question may be motivated by the expectation that the unique (and almost outlying) minimum of four values should not equal the first quartile. By Tukey's definition of the boxplot, 6 total visits would be at the very bottom of an obvious lower whisker. This seems to be how R does it, too, as can be seen with boxplot(x <- c(6, 17, 20, 25)); stripchart(x, v=TRUE, add=TRUE, col="Red"). $\endgroup$ – whuber Aug 22 '13 at 14:26
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    $\begingroup$ SS_11, have you shown us all the data or not? For why this is important, please see the preceding comment by @Nick Cox. $\endgroup$ – whuber Aug 22 '13 at 14:29
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    $\begingroup$ I am sorry..The dataset that I have shown here is just an example of how my table looks. There are more than a million rows of data and the box plot that R created out of the entire data set has no lower whisker. $\endgroup$ – SS_11 Aug 22 '13 at 14:50
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There is a simple story explaining all this. In fact all the evidence needed is in the question!

  1. The minimum observed value is 1.

  2. At least 25% of the observed values are 1, so the lower quartile is also 1.

  3. There is in principle a whisker connecting the lower quartile 1 and the lowest smaller value within 1.5 IQR, also 1. But the whisker is of zero length, between 1 and 1, and necessarily hard to see.

A simpler formulation is this: no whisker will be visible if the lower quartile is equal to the minimum, or if the upper quartile is equal to the maximum. (There are other cases in which no whisker is visible.)

Not the question here, but when data are this skewed, other displays are likely to be more helpful, such as a histogram or a quantile plot.

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