Mathcad 2.x and 3.x Boxplot issue

[shilbrand]

Hello Guys,

i got a question, maybe im doing something wrong but....

When i try to use the function boxplot(Data) the Q1 and Q3 are wrong. But the Median is right.

Example:

Q1 = 1.25 and Q3=3.75

BUT

Q1 should be 1.5 and Q3 should be 3.5, am i wrong?

Q1= (1+2)/2 = 2.5 and Q3=(3+4)2=3.5

If you want to see it in Mathcad, its in the Attach

Thanks and regards

Samuel

[LucMeekes]

There are multiple methods to calculate the quartiles. See Quartile - Wikipedia.

The question is what definition Prime uses.

Luc

[LucMeekes]

But none of the three methods described by Wikipedia results in Q1=1.25 and Q3=3.75.

Also note that the median is not the average. The median is that value that divides the set of numbers into two equally large sets.

So the median of the example set of values is 2.5, not because (2+3)/2=2.5, but because two values lie below 2.5 and two values lie above it.

In fact, for this set, the median could be anywhere between (but NOT including ! ) 2 and 3.

The same goes for the quartiles. Q1 is defined such that 1/4 of the values lie below it, and 3/4 lie above. Likewise, but reverse for Q3.

The boxplot function may have taken the extremes, added them and divided the result by 4 (for Q1) 2 (for the median) and 3/4 (for Q3).

That would give the results as displayed. Unfortunately I can't check.... Express limitation.

Luc

[LucMeekes]

Ah, probably a better guess is that Prime uses the minitab method from:

Quartile -- from Wolfram MathWorld

Luc

[shilbrand]

thanks for your effort!