5 number summary vs mean and standard deviation

Question

Hello i have a few numbers and i want to describe them using the best tool for this case: Either the 5-number summary or the mean and the standard deviation.But since i am statistics newbie i dont know when 5NS is better than mean and SD.In this specific case we have the following numbers:

130 125 107 97 96 94 86 83 82 81 58 55 54 52 48 47 45 45 42 41 39 39 39 38 36 35 34

5NS give us :

 Minimum.   1st Quartile.   Median.     3rd Quartile.      Maximum. 
     34.0      40.0          52.0          84.5            130.0 

and mean with standard deviaton give us:

     mean=64 and standard devation = 26.19

Which one is better to describe our data in this case and when is 5NS better to use than Mean and SD??

Answer 1

The answer to "what is the best way to describe data" is really "it depends on what you want to do with the description". In this case, with only about 25 numbers, you could easily show them all in a histogram. That will give your reader a way to see the shape of the distribution:

It's so irregular that perhaps no summary statistics do it justice.

Answer 2

They really tell you different things. For example, the five number summary does not tell you the mean, nor do the mean/SD tell you the median.

As another example, note that 130 and 125 are probably outliers. You can see from the five number summary that this is the case (at least for 130) since it is so much further away from the median than is the lowest value. The SD doesn't really give you any information about outliers, although its magnitude certainly indicates that the data are spread out. But note that the SD would be unchanged if 130 and 125 were outliers on the low side (as far below the mean as they are currently above the mean), while the five number summary would be very different.