# Name for (maximum+minimum)/2 and relationship to average?

Is there a common name for $$c := \frac{max(X)+min(X)}{2}$$? What is the relationship between $$\tilde{x} := Avg(X)$$ and $$c$$? What metrics or information can I derive from $$\tilde{x}$$ and $$c$$?

If I have $$C := \{c_{i}|1 \leq i \leq \frac{|X|}{2}; c_{i} := \frac{max_{i}(X)+min_{i}(X)}{2}\}$$ where $$max_{i}$$ is the i-th maximum and $$min_{i}$$ is the i-th minimum ($$max_{2}$$ would be the second largest element). What can I derive from $$C$$? $$|X|$$ here means the amount of samples/values in $$X$$.

• The quantity you refer to is called the midrange. See: en.wikipedia.org/wiki/Mid-range Commented Nov 11, 2018 at 19:15
• $E(c) = E(\bar X)$ if the distribution is symmetric. Otherwise $E(c)$ and $E(\bar X)$ can be used to indicate degree of skewness of the distribution of $X$. BTW, what is $|X|$? Commented Nov 11, 2018 at 20:36
• $|X|$ is the number of elements in $X$. Commented Nov 11, 2018 at 21:59
• Maybe you should add |X| into your question. At least, I think it is kind of absolute value. Commented Nov 12, 2018 at 0:18

- compbiostats