Astock has had returns of −18.5 percent, 28.5 percent, 18 percent, −9.6 percent, 34.3 percent, and 26.5 percent over the last six years. what are the arithmetic and geometric returns for the stock? (do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e. g., 32.16.) arithmetic average return % geometric average return %

The arithmetic average of a group of numbers is their sum divided by the number of them.

arithmetic average = (-18.5 +28.5 +18 -9.6 +34.3 +26.5)%/6 = 13.20%

(Please note that it is meaningless to compute an arithmetic average of percentages that have different base values, as these do. It may be a decent exercise in arithmetic, but the result has no real-world meaning whatever.)

The geometric mean of a set of n numbers is the n-th root of their product. Because these are stock returns, we aren't really interested in the geometric mean of the given percentages. (Such a mean of a set including negative numbers has no meaning in any event.) What we want to find is the geometric mean of the year-to-year multiplier of stock values. Then we want to convert that back to a rate of return.

... ((1-.185)(1+.285)(1+.18)(1-.096)(1+.343)(1+.265))^(1/6) ≈ 1.89791917^(1/6) ≈ 1.112703

This multiplier value of 1.1127 corresponds to a

... geometric average return = 11.27%

probability for j is 1/4

while

a is 1/6

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.