# Assigning weights to a list of averages when all I have is the mean, standard deviation, and number of samples

I have some data which, essentially, gives the change in value of a particular stock option according to 1 movement in price of the underlying stock value.

For example, say stock 'ABC' has 4 different stock options (don't worry about the details), 1, 2, 3, and 4.

When ABC moves in value by \$1, then stock options 1-4 change by a certain amount. What I have is a list of data indexed by date, that tells me how much options 1-4 changed that day compared to the change in the value of ABC. Not every day has data, so some days have null values

The source data looks something like this:

           1.    2.   3.   4
---------------------------
1-1-20.   NONE  .5   1   .9
1-2-20.   .3   NONE  1   .8
1-3-20.   NONE  .3   1   .8


I averaged all of this data and get a table like:

1-avg.   1-std.   1-count.   2-avg.   2-std.  2-count... etc...

.3      0         1         .3        .2      2


Where avg is the average, std is the standard deviation, and count is the number of samples with real (non-null) values.

My question is, how can I weight the averages according to std and count so that, for instance, if I'm trying to find the HIGHEST average, I can make a determination where, if I have two choices: an average of 10, with a standard dev of 10, and a count of 3....versus an average of 8 with a standard dev of 2 and a count of 100....that I can quantify that the average of 8 is probably a better value because it has a higher count and a lower std.

Is there maybe a quick and dirty calculation I can do?