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I want to determine the distribution from the EMFIT QS sleep data which gives only min, max and mean values for sleep clasess in R, in order to estimate quartiles. Types of sleep waves in the signal in Fig. 1. I know the thread answer Finding Quartiles in R. Fig. 1 types of possible sleep waves (source Guyton Physiology).

enter image description here

Summary of the descriptive statistics given by the manufacturer given for one measurement session lasting 5-14 hours

dat.m <- structure(list(Vars = structure(c(1L, 3L, 2L), .Label = c("Average ", 
"Max     ", "Min     "), class = "factor"), Sleep = c(7, 4, 10
), Awake = c(12L, 5L, 15L)), .Names = c("Vars", "Sleep", "Awake"
), class = "data.frame", row.names = c(NA, -3L))

> dat.m
      Vars Sleep Awake 
1 Average      7    12
2 Min          4     5
3 Max         10    15

Current method to estimate the quartiles is manual

#https://stackoverflow.com/a/44043313/54964
quartiles <- data.frame(Vars = c("Q1","Q3"), Sleep = c(6,8), 
                    Awake = c(9,13))

OS: Debian 8.7
R: 3.4.0 (backports)
Related therad: Why this CSV data complicates with ggplot2 whisker plot?

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    $\begingroup$ Note that min, max and mean tell you very little about the quartiles -- see here and similar issues occur as here or here. $\endgroup$ – Glen_b May 20 '17 at 16:26
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    $\begingroup$ Please ask a more specific question; you'll need to make some assumptions to get much value from this. Why would your "rough proposal" make any sense? please explain your thinking. $\endgroup$ – Glen_b May 20 '17 at 16:30
  • $\begingroup$ @Glen_b Please, open again. I need to determine the underlying distiribution to propose anything about the quartiles. $\endgroup$ – Léo Léopold Hertz 준영 May 21 '17 at 3:36
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    $\begingroup$ The first link I gave already discusses the difficulty of trying to do this from just those values (if it was possible to determine the distribution from min, max and mean, finding quartiles would be easy); you edit has made it even more clearly a duplicate of that post. You need to bring information from outside the data (like knowledge of the kind of variable you're dealing with might suggest a parametric form, or subject area knowledge may give information about shape for example) to have any hope of doing very much at all. $\endgroup$ – Glen_b May 21 '17 at 4:27
  • $\begingroup$ @Glen_b Please, see the body and open. I made it more descriptive of the situation. $\endgroup$ – Léo Léopold Hertz 준영 May 21 '17 at 7:02