Geometric and weighted mean, comparative pie charts and capture/recapture method

Question 1

What is the formula for weighted mean?

Answer 1

Σ(value x weight) / Σweights

Σwx / Σw

Question 2

What is the formula for geometric mean?

Answer 2

ⁿ/value₁ x value₂ x … x value_n

^{^ nth route}

Question 3

When are comparative pie charts used?

Answer 3

To compare two sets of data

Question 4

How does the area of comparative pie charts relate to the total frequencies?

Answer 4

They must be in the same ratio

Question 5

What is the formula for calculating the missing ratio of a comparative pie chart? (When given the Σfrequencies and another ratio)

Answer 5

r₂ = r₁ x ((²/F₂) / (²/F₁))

radius 2 = radius 1 x ((square root of Σ frequency 2) / (square root of Σ frequency 1))

Question 6

When is the Petersen capture-recapture method used?

Answer 6

To estimate the size of a population, where it would be impossible to capture all the animals within the population to count

Question 7

What is the Petersen capture-recapture formula?

Answer 7

m/n = M/N

N = Mn/m

m = no. marked in second sample

n = no. caught in second sample

M = no. given tags in first sample

N = total population

Question 8

What assumptions are made for the Petersen capture-recapture method?

Answer 8

The population hasn’t changed - no members have entered or left, and there have been no births or deaths

The probability of being caught is equal for all individuals

Marks/tags are not lost and are always recognisable

The sample size is big enough to be representative of the population