Finding standard deviation using only mean, min, max?

standard-deviation
user1580957 picture user1580957 · Aug 21, 2012 · Viewed 34.9k times · Source

I want to find the standard deviation:

Minimum = 5
Mean = 24
Maximum = 84

Overall score = 90

I just want to find out my grade by using the standard deviation

Thanks,

Answer

bames53 picture bames53 · Aug 21, 2012

A standard deviation cannot in general be computed from just the min, max, and mean. This can be demonstrated with two sets of scores that have the same min, and max, and mean but different standard deviations:

  • 1 2 4 5 : min=1 max=5 mean=3 stdev≈1.5811
  • 1 3 3 5 : min=1 max=5 mean=3 stdev≈0.7071

Also, what does an 'overall score' of 90 mean if the maximum is 84?

Related questions

Standard deviation of a list

I want to find mean and standard deviation of 1st, 2nd,... digits of several (Z) lists. For example, I have A_rank=[0.8,0.4,1.2,3.7,2.6,5.8] B_rank=[0.1,2.8,3.7,2.6,5,3.4] C_Rank=[1.2,3.4,0.5,0.1,2.5,6.1] # etc (up to Z_rank )... Now I want to take the mean and std …

Read More
Add error bars to show standard deviation on a plot in R

For each X-value I calculated the average Y-value and the standard deviation (sd) of each Y-value x = 1:5 y = c(1.1, 1.5, 2.9, 3.8, 5.2) sd = c(0.1, 0.3, 0.2, 0.2, 0.4) plot (x, y) How can I use the standard deviation to add error bars to each datapoint of my …

Read More
How to calculate standard deviation using JAVA

I'm very new here, at the moment I am trying to calculate standard deviation with Java (I have googled it haha) but I am having a lot of issues on getting it working I have ten values that are inputed …

Read More