logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XI  >>  Math  >>  Statistics
0 votes

Standard deviations for first 10 natural number is

$\begin{array}{1 1}(A)\; 5.5 \\(B)\;3.87 \\(C)\;2.97 \\(D)\;2.87 \end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • The formula to calculate SD is $SD= \sqrt {\large\frac{\sum x^2}{n} - \bigg( \large\frac{\sum x}{n}\bigg)^2}$
1st 10 natural numbers are 1,2,3,4,5,6,7,8,9,10
$\sum x = 1+2+3+4+5+6+7+8+9+10$
$\qquad = \large\frac{n(n+1)}{2} =\large\frac{10(10+1)}{2}$
$\qquad=\large\frac{10 \times 11}{2} $$=55$
$\sum x^2 =1^2+2^2+..............+10^2$
$\qquad= \large\frac{n(n+1)(2n+1)}{6}$
$\qquad= \large\frac{10 \times 11 \times 21}{6}$
$\qquad= 385$
$SD= \sqrt {\large\frac{\sum x^2}{n} - \bigg( \large\frac{\sum x}{n}\bigg)^2}$
$\qquad= \sqrt {\large\frac{385}{10} - \bigg( \large\frac{55}{10}\bigg)^2}$
$\qquad= \sqrt {38.5 -(5.5)^2}$
$\qquad= \sqrt {8.25 }$
$\qquad= 2.87$
Hence D is the correct answer.
answered Jul 8, 2014 by meena.p
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...