Answer to Question #166846 in Optics for Abdul

Question

Polly has 50 rose bushes. She counts the number of flowers on 10 of them.

The number of flowers on each rose bush is:

9, 2, 5, 4, 12, 7, 8, 11, 9, 3

Find the standard deviation of the number of flowers on a rose bush. State your answer to 1 decimal place.

Answer 1

Data: 9,2,5,4,12,7,8,11,9,3

n= 10

Mean$(\bar x) = \dfrac{9+2+5+4+12+7+8+11+9+3}{10}=\dfrac{70}{10}=7$

Variance($\sigma^{2}$ )= $\dfrac{\Sigma_{i=1}^{10}(x_i-\bar x)^2}{n}$

$= \dfrac{2^2+(-5)^2+(-2)^2+(-3)^2+5^2+0+1^2+4^2+2^2+(-4^2)}{10}$

$= \dfrac{104}{10}=10.4$

Standard Deviation$(\sigma)= \sqrt{Variance}$

$=\sqrt{10.4}$

= 3.22

So, standard deviation of the number of flowers on a rose bush is 3.2