The mean value or the average is calculated by adding all the measurements and dividing the sum by the total number of measurements.
Mean = sum of the bristles / the total number of individuals
Sum of the bristles = 1+ (4×2) + (7×3) + (31×4) + (56×5) + (17×6) + (4×7)
= 564
Total number of individuals = 1+ 4 + 7 + 31 + 56 + 17 + 4 = 120
Mean = 564 / 120 = 4.7 bristle/individual
The variance can be calculated like this.
S2 = 1/n?(xi-x)2
n = total number of individuals = 120
xi = number of bristles
x = average number of bristle/individual = 4.7
Variance = 1/120?[(14.7)2+(2-4.7)2+(3-4.7)2+(4-4.7)2+(5-4.7)2+(6-4.7)2+(7-4.7)2]
= 0.26
Variance s2 = 0.26
The amount of variation in a population can be quantified using variance.
The standard deviation can be calculated as follows.
The standard deviation(s) is the square root of the variance (s2).
The square root of 0.26 = 0.51
The standard deviation is used to quantify the extent of deviation from the mean.