
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 1st, 2017, 08:09 AM  #1 
Member Joined: Mar 2017 From: Israel Posts: 33 Thanks: 2  Range
Hello Can you help me please about the following exercise: The variance of two numbers is 25, therefore, their range is: a. 5 b. 10 c. 25 d. The range can not be calculated without knowing numbers. e. None of the answers is correct. I think the answer is d, but I'm not sure :\ Variance: https://en.wikipedia.org/wiki/Variance If you didn't understand, I will explain again (I'm not from country where people speak english, and sorry if my english is bad). Thanks a lot! Last edited by IlanSherer; August 1st, 2017 at 08:11 AM. 
August 1st, 2017, 08:41 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,959 Thanks: 801 
A crucial point here is that the problem says "two number". If there were more than two numbers, then (d) would be correct. But knowing that there are exactly two numbers, and letting those two numbers be "m" and "n" (we can take "n" to be the larger), then we know that their mean is $\displaystyle \frac{m+ n}{2}= \frac{m}{2}+ \frac{n}{2}$. The variance then is given by $\displaystyle (m \frac{m}{2} \frac{n}{2})^2+ (n \frac{m}{2} \frac{n}{2})^2$$\displaystyle = (\frac{m}{2} \frac{n}{2})^2+ (\frac{n}{2} \frac{m}{2})^2= 2(\frac{m}{2} \frac{n}{2})^2= \frac{1}{2}(n m)^2$ Now, suppose that is 25: then $\displaystyle (n m)^2= 50$ so, since n> m, $\displaystyle n m= 25\sqrt{2}$. I would say the correct answer is (e). Last edited by Country Boy; August 1st, 2017 at 08:44 AM. 
August 1st, 2017, 08:53 AM  #3 
Member Joined: Jan 2017 From: California Posts: 80 Thanks: 8 
$s\approx \frac{range}{4}$ Therefore, $range\approx 20$ 

Tags 
range 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Range of k  panky  Trigonometry  3  November 1st, 2016 05:22 PM 
range of x,y,z  panky  Algebra  6  June 15th, 2016 01:58 PM 
Calculating a position in a range while limiting the range  tale  Computer Science  5  May 23rd, 2012 06:16 AM 
range of f(x)  panky  Calculus  0  March 20th, 2012 06:30 AM 
Range of f(x)  stuart clark  Calculus  7  April 24th, 2011 01:01 PM 