1. ## Averaging discrete variables

I'm doing some data analysis for an experiment that I conducted involving serial dilutions.

Because of the nature of the experiment, my variable of interest (MIC), can take on discrete values of:
15, 7.5, 3.75... 15/(2^i) where i = 0, 1, ..., n.

Now, I'm a little confused. I have done triplicates of the experiment, and I was about to average the data. But I'm not sure if it makes sense to average discrete values such as these (I'm ok averaging discrete values of 1,2,3,4 etc.)

Let's say I get values of 7.5, 3.75, and 3.75. Does averaging it even make sense?

Hope someone can help me. I've been trying to figure it out. Thanks!

2. Originally Posted by xtrios
I'm doing some data analysis for an experiment that I conducted involving serial dilutions.

Because of the nature of the experiment, my variable of interest (MIC), can take on discrete values of:
15, 7.5, 3.75... 15/(2^i) where i = 0, 1, ..., n.

Now, I'm a little confused. I have done triplicates of the experiment, and I was about to average the data. But I'm not sure if it makes sense to average discrete values such as these (I'm ok averaging discrete values of 1,2,3,4 etc.)

Let's say I get values of 7.5, 3.75, and 3.75. Does averaging it even make sense?

Hope someone can help me. I've been trying to figure it out. Thanks!
Is each value equally likely to occur? What are you trying to achieve by finding an average of the measured values?

The problem as presented is too vague.

3. Hi

The test I'm doing is an assay with 2x serial dilution. I am trying to determine the minimum inhibitory concentration of an antibiotic against a bacteria strain. The concentration values of the antibiotic across the 10 wells decreases by 2x in each well. Hence with a starting value of 15 ug/mL, the next is 7.5, 3.75 and so on. Due to the nature of the assay, the minimum inhibitory concentration is the smallest value that has no bacteria growth.

Hence if the 1.875 ug/mL is the first well with bacteria growth (10, 7.5 and 3.75 have no growth), 3.75ug/mL is the experimental minimum inhibitory concentration.

So if my experiment yields MICs of 7.5, 3.75 and 3.75, does it make sense to average it?

Hope this is clear. Thanks for the help!

4. Originally Posted by xtrios
Hi

The test I'm doing is an assay with 2x serial dilution. I am trying to determine the minimum inhibitory concentration of an antibiotic against a bacteria strain. The concentration values of the antibiotic across the 10 wells decreases by 2x in each well. Hence with a starting value of 15 ug/mL, the next is 7.5, 3.75 and so on. Due to the nature of the assay, the minimum inhibitory concentration is the smallest value that has no bacteria growth.

Hence if the 1.875 ug/mL is the first well with bacteria growth (10, 7.5 and 3.75 have no growth), 3.75ug/mL is the experimental minimum inhibitory concentration.

So if my experiment yields MICs of 7.5, 3.75 and 3.75, does it make sense to average it?

Hope this is clear. Thanks for the help!
I'd suggest you need to collect much more data before a sample mean can be meaningful.

5. My question is not an issue about collecting more data points actually. Let me rephrase the question.

If the variable can only take on values of, let's say 1, 10, 100, 1000 (instead of a continuous variable from 0 to 1000), can it be meaningfully averaged?

6. Originally Posted by xtrios
My question is not an issue about collecting more data points actually. Let me rephrase the question.

If the variable can only take on values of, let's say 1, 10, 100, 1000 (instead of a continuous variable from 0 to 1000), can it be meaningfully averaged?
It depends on what you want to use the average for.

If you roll a die (whether it be biased or unbiased) and note the number of spots each roll, you can obviously calculate the average number of spots. But the meaningfullness of this average depends on what you want to use it for ......

7. Well, but in a die roll, the numbers are evenly spaced: 1, 2, 3, 4, 5, 6. Let's say we have a die with number 1, 10, 100, 1000, 10000, 100000. Would that average even mean anything? (This may not be a great analogy, since probability governs a die roll, and not really the experiment)