The red-tailed tropic bird, Phaethon rubricauda, is an extremely rare sea bird that nests on several islands of the Queensland coast of Australia. As part of a conservation e ort to manage these endangered birds, every nesting pair was measured and weighed. Below are the body weights of these birds (in kg). Female 2.45 2.57 2.81 2.37 2.01 2.50 2.32
Male 2.86 2.65 2.75 2.60 2.30 2.49 2.84

Required:
a. Determine the following descriptive characteristics for the weights of the females: mean, variance, and standard deviation. Is this a sample or population? Again, pay attention to number of decimal places and appropriate units.
b. Determine the mean, variance, and standard deviation for the male weights.

This is a population

a) Female

Mean : 2.432857143kg

Variance: 0.05162040817kg

Standard deviation: 0.2272012504kg

b) Male

Mean : 2.641428571kg

Variance : 0.03432653062kg

Standard deviation: 0.1852742039kg

Step-by-step explanation:

a. Determine the following descriptive characteristics for the weights of the females: mean, variance, and standard deviation. Is this a sample or population? Again, pay attention to number of decimal places and appropriate units.

a) Female: 2.45 2.57 2.81 2.37 2.01 2.50 2.32

Mean

The formula = Sum of term/ Number of terms

Mean = 2.45 + 2.57 + 2.81 + 2.37 + 2.01 + 2.50 + 2.32/7

17.03/7

= 2.432857143kg

Variance

This is a population

Hence: The formula for Population variance =

= (X - Mean)²/N

Where N = Number of terms = 7

= (2.45 - 2.432857143)² + (2.57 -2.432857143)² + (2.81 -2.432857143)² + (2.37- 2.432857143)²+ (2.01 - 2.432857143)²+ (2.50 - 2.432857143)² + (2.32 - 2.432857143)² /7

= 0.0002938775509 + 0.01880816325 + 0.1422367347 + 0.003951020409 + 0.1788081633 + 0.004508163265 + 0.0127367347/7

= 0.3613428572/7

= 0.05162040817kg

Standard Deviation

Formula = √Variance

= √0.05162040817

= 0.2272012504kg

b. Determine the mean, variance, and standard deviation for the male weights

Male 2.86 2.65 2.75 2.60 2.30 2.49 2.84

Mean

The formula = Sum of term/ Number of terms

= 2.86 + 2.65 + 2.75 + 2.60 + 2.30 + 2.49 + 2.84/7

= 18.49/7

= 2.641428571 kg

Variance

= ( 2.86 -2.641428571)² + (2.65 - 2.641428571)² + (2.75 -2.641428571)² + (2.60 +2.641428571)² + (2.30 - 2.641428571)² + (2.49+2.641428571)² (2.84 + 2.641428571)²/7

= 0.0477734694 + 0.00007346938775 + 0.01178775511 + 0.001716326531 + 0.1165734694 + 0.02293061224 +! 0.03943061226/7

= 0.2402857143/7

= 0.03432653062kg

Standard Deviation

= √Variance

= √0.03432653062

= 0.1852742039kg

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.