Estimating Population Size Using Mark and Recapture Method
Practical 16: estimating Population Size Using Mark and Recapture Method
Raw and Processed Data
Table 1: Uncertainties of apparatus used in the experiment. Apparatus | Uncertainties | Stopwatch | ±0.01s |
Table 2: Formulae and sample calculations involved in processing data in the experiment. Calculations | Formula | Sample Calculation | Mean
( x ) | x = 1n i=1naiWhere, 1. n refers to the total number of values. 2. ∑ refers to the addition of all values starting with the first value, denoted by i = 1, and ending off with the last value, denoted by n. 3. ai refers to the values in sequence from i = 1 to the nth term or last term. | Mean Lincoln Index: x= 15114+127+194+163+172≈154 | Standard Deviation ( σ ) | σ=1ni=1nfi(xi-x)2Where, 1. n refers to the total number of values. 2. ∑ refers to the addition of all values starting with the first value, denoted by i = 1, and ending off with the last value –denoted by n. 3. fi refers to the frequency of that exact term being calculated. 4. (xi-x)2 refers to the square of the term, denoted by xi, subtracted by the mean value of the terms, denoted by x. | Standard Deviation for Lincoln Index: σ= 15(114-1542+127-1542+194-1542+163-1542+(172-154)2)≈33.0 | Lincoln Index (Total Population) | Total Population =x1-x2x3 Where, 1. x1 refers to the number Of white beads in the first capture. 2. x2 refers to the total number of white and red beads in the second capture. 3. x3 refers to the number of red beads in the second capture | Total Population of white beads (1st replicate):19×122=114 | Chi Squared Test | x2 = i=1n(Oi-Ei)2EiWhere, 1. x2 refers to the Pearson’s cumulative test statistic. 2. ∑ refers to the addition of all values generated. 3. i refers to the degrees of freedom. 4. n refers to the number of different types of appearance. 5. Oi refers to the observed frequencies. 6. Eirefers to the expected frequencies. | Chi Squared Value for the use of Lincoln index to calculate
Raw and Processed Data
Table 1: Uncertainties of apparatus used in the experiment. Apparatus | Uncertainties | Stopwatch | ±0.01s |
Table 2: Formulae and sample calculations involved in processing data in the experiment. Calculations | Formula | Sample Calculation | Mean
( x ) | x = 1n i=1naiWhere, 1. n refers to the total number of values. 2. ∑ refers to the addition of all values starting with the first value, denoted by i = 1, and ending off with the last value, denoted by n. 3. ai refers to the values in sequence from i = 1 to the nth term or last term. | Mean Lincoln Index: x= 15114+127+194+163+172≈154 | Standard Deviation ( σ ) | σ=1ni=1nfi(xi-x)2Where, 1. n refers to the total number of values. 2. ∑ refers to the addition of all values starting with the first value, denoted by i = 1, and ending off with the last value –denoted by n. 3. fi refers to the frequency of that exact term being calculated. 4. (xi-x)2 refers to the square of the term, denoted by xi, subtracted by the mean value of the terms, denoted by x. | Standard Deviation for Lincoln Index: σ= 15(114-1542+127-1542+194-1542+163-1542+(172-154)2)≈33.0 | Lincoln Index (Total Population) | Total Population =x1-x2x3 Where, 1. x1 refers to the number Of white beads in the first capture. 2. x2 refers to the total number of white and red beads in the second capture. 3. x3 refers to the number of red beads in the second capture | Total Population of white beads (1st replicate):19×122=114 | Chi Squared Test | x2 = i=1n(Oi-Ei)2EiWhere, 1. x2 refers to the Pearson’s cumulative test statistic. 2. ∑ refers to the addition of all values generated. 3. i refers to the degrees of freedom. 4. n refers to the number of different types of appearance. 5. Oi refers to the observed frequencies. 6. Eirefers to the expected frequencies. | Chi Squared Value for the use of Lincoln index to calculate