Answer :
Answer:
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