descriptive statisticsstatistics
I am drawing a box plot for a question where the data set is the bulb life time(in hours)
My 5 number summary is
Q1 : 208.25
Q2 : 297
Q3 : 376.5
min : 172
max : 1020
IQR : 168.25
3/2 * IQR : 252.375
Upper Bound : 628.875
Lower Bound : -44.125
Since the data set is about time, I know I can not use negative values,so what should I use as my negative value, I know I won't get any outliers here but still I'm curious.
Perhaps it's more evocative if we draw it slightly differently. Think of the single line and horizontal lines as an abstract version of this (Kazimir Malevich would be so proud).
In any case, the further you go in mathematics the lazier mathematicians get in naming things. Shout outs to "admissible", "pseudo / quasi / weak", and the horrors of "normal" and "regular".
If there were just one light bulb with an average lifetime of $1000$ hours, then the number of failures in time $t$ would have a Poisson distribution with expected value $t/1000$. With $10$ light bulbs functioning independently of each other, that expected value is simply multiplied by $10$. The reason is that the distribution of the sum of independent Poisson-distributed random variables is Poisson-distributed. I think the question of why that is so has been answered here a number of times.
Best Answer
Never plot a box-whisker plot beyond min and max of data. Upper and lower bound are just used to find out outliers and extreme outliers. In this case you have to take lower bound as 172. You can use MATLAB command :
boxplot(x)to check the same rule.