1. Who seems to have more variability in their shoe sizes, men or women? a) Men b) Women c) Neither group show variability d) Flag this Question 2. In

Joni Kenny 2021-06-13 Answered
1. Who seems to have more variability in their shoe sizes, men or women?
a) Men
b) Women
c) Neither group show variability
d) Flag this Question
2. In general, why use the estimate of n1 rather than n in the computation of the standard deviation and variance?
a) The estimate n-1 is better because it is used for calculating the population variance and standard deviation
b) The estimate n-1 is never used to calculate the sample variance and standard deviation
c) n1 provides an unbiased estimate of the population and allows more variability when using a sample and gives a better mathematical estimate of the population
d) The estimate n-1 is better because it is use for calculation of both the population and sample variance as well as standard deviation.
Shoe Size (in cm)Gender (M of F)25.7M25.4F23.8F25.4F26.7M23.8F25.4F25.4F25.7M25.7F23.5F23.1F26M23.5F26.7F26M23.1F25.1F27M25.4F23.5F23.8F27M25.7F
Shoe Size (in cm)Gender (M of F)27.6M26.9F26F28.4M23.5F27F25.1F28.4M23.1F23.8F26F25.4M23.8F24.8M25.1F24.8F26M25.4F26M27M25.7F27M23.5F29F
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Expert Answer

timbalemX
Answered 2021-06-14 Author has 108 answers

Step 1
We have to show whose shoe size shows maximum variability ic (man of female).
We will compute CV (coefficient of variation) for this purpase and accordingly give the result.
Firstly we will compute for males
Shoe size (in cm)(xix¯)225.70.960426.70.000425.70.9604260.4624260.4624270.1024270.102427.60.846428.44.665628.44.665625.41.638424.83.5344260.4624260.4624270.1024270.1024295.3824
Total =435.7
Mean(x¯)=TotalNumber of Observation
=453.717
=26.68
Variance(σ2)=1n(xix¯)2
=117(xix¯)2
=26.756417
1.57=1.57
CV=σx¯×100
=1.5726.68×100=4.696
Step 2
Now, we will compute for females
Shoe size (in cm)(xix¯)225.40.756923.86.100925.40.756923.86.100925.40.756925.40.756925.70.324923.57.672923.110.048923.57.672926.70.184923.110.048925.11.368925.40.756923.57.672923.86.100925.70.324926.90.3969260.072923.57.6729270.532925.11.368923.110.048923.86.1009260.072923.86.100925.11.368924.82.160925.40.756925.70.324923.57.6729
Total =814.6
x¯=814.631=26.27
σ2=1n(xix¯)2
=112.059931=3.614
σ=3.614=1.90
CV=1.9026.27×100
=7.23
Step 3
Answer (1): If we look at CV of the both males and females.
The more variability is in female shoe size as compared to male shoe size.
So option (B) is correct.
Answer (2): (n1) provides an umbiased estimate of population and allouss more variability when using a sample and gives a better mathematical estimate of the population.
Option (C) is correct.

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