What does an increase in the mean, but the median is the same signify? I have been collecting some



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What does an increase in the mean, but the median is the same signify?
I have been collecting some data from a project (check if something is affected by the environment it is in) using some sensors. I collected some data before making a change in the environment and then after. My hypothesis is that it should be affected by the environment (the number must decrease).
To test this, I did some calculations (in Excel) and noticed that there is a small increase in the mean, but the median remains the same. I don't know how to interpret this (I only have some basic knowledge about statistics). Can I simply assume that there was indeed an increase (and that my hypothesis is false), or is there something more to it? After searching online, I found something about called "hypothesis testing of means" that seems to be applicable here, but I have to idea how to do this (tried watching videos about it, but didn't understand how to use it in my case). I calculated the variance and the standard deviation if it helps. Thanks.
Here is the result of my data:
Sample size: 60
mean: 3.35
median: 3.5
variance: 0.25
standard dev.: 0.50
mean: 3.51
median: 3.5
variance: 0.20
standard dev.: 0.45

Answer & Explanation



Beginner2022-06-28Added 29 answers

A single new large data point will increase the mean but leave the median the same. Think about what happens to the salary distribution in a company if the CEO gets a giant raise.
To know the "meaning" of your observation we need a lot more context. An Excel plot of the data should help you.
That said, this is a better question for stats.stackexchange.com.

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