Consider the numbers 1 1 3 4 5

Question

If the numbers represent laps around the track, which measure(s) of center would make the most sense? 

 

If the numbers represent waitresses at a diner, which measure(s) of center would make the most sense ?

 

if the numbers represent survey responses with 1=disagree strongly 2= disagree 3= agree 4=agree strongly 5= agree very strongly. Which measure(s) of center would make the most sense ? 

Answer 1

First, consider the mean, the median, and the mode as the measures of central tendency.

 

Now, create a frequency distribution:

 

   1:     ****  ****

   2:

   3:     ****

   4:     ****

   5:     ****

 

The mean is the arithmetic average: ( (1+1+3+4+5)/5)= 14/5 ).

The median is the half-way point:   3   (2 observations below and 2 above).

The mode has the greatest frequency:    1

 

The first, key observation is that these numbers are quite different.  Except for the missing 2, they are uniformly distributed.  That means there is not much "central tendency" to talk about.  So, if the goal is uniformity (for example track team members number of practice laps), then these results are disappointing.  However, if the goal is progress (for example one person's number of laps each of five days), then there is steady progress.

 

So, the expectations establish what "makes the most sense".

 

Now, consider range, standard deviation and variance.  They measure the "spread" of the observations.  For this data, these are important since they indicate "non clustered" data.

 

You must decide what the expectations are for each situation mentioned, and what additional stats to "make sense" in a summary of the data.