How to calculate mean and standard deviation from median and quartiles I have 1st quartile, median and 3rd quartile. I want to find mean and SD. I want to use Bland’s method1 but i do not have max, min values of the data. How can i solve this problem? Is there any R package?
1 Bland, Martin. 2014. “Estimating Mean and Standard Deviation from the Sample Size, Three Quartiles, Minimum, and Maximum.” International Journal of Statistics in Medical Research 4 (1): 57–64.
 A: Adding to Michael Chernick's comment, here's an example.
x <- runif(1000,0,1)
summary(x)  #1st Q = 0.27  3rd = 0.77  mean = .51

x1 <- c(x,100)
summary(x1) #1Q = 0.27  3rd = 0.77  mean = .61

x2 <- c(rnorm(100,0,1), rnorm(10,10,.1))
summary(x2)  # 1st = -.85  3rd = 0.69, mean = 0.71

With the first pair, note that a single outlier affects the mean but not the quartiles.  The last example is one where the mean is larger than the 3rd quartile. 
One real world case where the mean could be greater than the third quartile is income. 
A: There is a detailed publication on this topic from Greco et al, How to impute study-specific standard deviations in meta-analyses of skewed continuous endpoints? World Journal of Meta-Analysis 2015;3(5):215-224.
The main findings of this work are that it is acceptable to approximate "missing values of mean and SD with the correspondent values for median and interquartile range".
A: You can check Wan et al. (2014)*. They build on Bland (2014) to estimate these parameters according to the data summaries available. See scenario C3 in their paper :
$$ \bar{X} ≈ \frac {q_{1} + m + q_{3}}{3}$$
$$ S ≈ \frac {q_{3} - q_{1}}{1.35}$$
or, if you have the sample size :
$$ S ≈ \frac {q_{3} - q_{1}}{2 \Phi^{-1}(\frac{0.75n-0.125}{n+0.25}) }$$
where $q_{1}$ is the first quartile, $m$ the median, $q_{3}$ is the 3rd quartile and $\Phi^{-1}(z)$ the upper zth percentile of the standard normal
distribution.
So, in R :

q1 <- 0.02
q3 <- 0.04
n <- 100

(s <- (q3 - q1) / (2 * (qnorm((0.75 * n - 0.125) / (n + 0.25)))))
#[1] 0.0150441


* Wan, Xiang, Wenqian Wang, Jiming Liu, and Tiejun Tong. 2014. “Estimating the Sample Mean and Standard Deviation from the Sample Size, Median, Range And/or Interquartile Range.” BMC Medical Research Methodology 14 (135). doi:10.1186/1471-2288-14-135.

A: I faced similar problem , where i calculated percentiles (0 to 100%) and then I was asked to give back mean as well , after playing in my notebook i noticed that the empirical mean of the quantiles list is in fact the mean of the distribution , thought i discovered a new theorem hahah but then found this
https://en.wikipedia.org/wiki/Inverse_transform_sampling
The theorem established that if you consider F-1 X(w) a random variable and you sample randomly in [0,1] then take the corresponding X , you can generate samples this way from the original distribution , that's why i was getting the mean when computing the quantiles mean .
It's not mentioned directly but if you can generate samples of the original distribution then their mean is the mean of the original distribution .
