Question

The numbers of beans in some cocoa pods
are 30, 28, 30, 35, 40, 25, 32, 36, 38 and 40.
a Calculate the mean number of beans per
cocoa pod.
b Calculate the standard deviation of the
distribution.​

Answer 1

Answer:

a) Mean number of beans = 33.4 per coco pad

b) Standard deviation of the  beans = 5.2   per coco pad

Step-by-step explanation:

Step(i):-

a)

Given data  30, 28, 30, 35, 40, 25, 32, 36, 38 and 40.

mean of beans

  x⁻ = ∑x/n

$x^{-} = \frac{30+ 28+30+35+40+25+32+36+38 + 40.}{10} = 33.4$

Mean number of beans per coco pad  = 33.4

step(ii):-

b)

standard deviation

∑(xi - x⁻)²  =  (30-33.4)²+ (28-33.4)²+(30-33.4)²+(35-33.4)²+(40-33.4)²+(25-33.4)²+(32-33.4)²+(36-33.4)²+ (38-33.4)²+(40-33.4)²

On calculation , we get

      ∑(xi - x⁻)²  = 242.4

standard deviation

 =        $\sqrt{\frac{sum((x-x^{-} )^{2} }{n-1} } = \sqrt{\frac{242.4}{10-1} } = 5.189$

Standard deviation of the  beans  (σ) = 5.2   per coco pad