University Statistics Assignment: Variability Relative to the Mean

This statistics assignment analyzes variability relative to the mean using various datasets. The student explores waist, thigh, abdominal, and bicep girth measurements, comparing male and female distributions, skewness, and overlap. The assignment calculates typical measurements using mean and standard deviation, and also uses quartiles to determine suitable intervals for unisex measurements, such as belt sizes. Furthermore, the assignment examines heart rate data, comparing male and female values and variability, and proposes using quartiles for defining normal heart rate intervals. The analysis supports the use of different ranges for men and women due to inherent differences in heart rates, as indicated by the data provided.

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Student’s Name
Instructor’s Name
Institution
Course
Date
Quantifying variability relative to the mean
Question 1
Part A
For the four variables, in essence, the waist, thigh, abdominal, and the bicep girths, it can
be argued that the waist girth variable tends to be larger for male than for female. The reason is
that the distribution for the male is skewed to the right (positively skewed) more than for the
distribution for female compared to all the variables as shown below.
Part B
Among the four variables, the thigh girth tend to be about the same size for both the male
and the female since the distribution for both the male and female has nearly similar degree of

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skewedness in positive and negative direction making them almost to overlap as shown in the
figure.
Part C
The table below presents the typical measurements to determine the overlap in
distribution of the variables between men and women using the sum of the mean and the SD.
Typical measurements (Mean ± SD) for male and female
Variable Male Female Substantial overlap (Yes/ No)
Waist girth 93.3 77.4 No
Thigh girth 60.8 61.8 Yes
Abdominal girth 96.1 93.6 No
Bicep girth 37.4 30.8 No
Part D
From the findings in part C, it can be argued that the obtained results support those in
parts A and B because the interval of the typical measurements have the most enormous

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difference for the waist girth variable among the entire variables indicating that the waist girth
for men is quite more extensive compared to women. On the other hand, the distribution for the
thigh girth for the male is seen to overlap with that of the female as indicated by a tiny difference
in the typical measurements (mean ± SD) between the men and women that fall within the ±1
range.
Question 2
Part A
The interval of typical measurements for the waist girth using quartiles.
Male First Quartile, Q1 Third Quartile, Q3
Female 64.7 72.8
Male 77.9 90
To obtain the typical waist interval measurement for a unisex one-size-fits belt for all the adults,
the range should be within the lowest value of Q1 and the highest value of Q3 thus giving the
interval range of 67.4 – 90 for the belts.
Part B
An interval of typical measurements using mean and SD as obtained from part C of
question two lies within the range of 77.4 – 93.3 for the unisex belts for all adults.
Variable Male Female
Waist girth 93.3 77.4
Part C

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Based on the two intervals, the interval calculated from the quartiles would be the most
suitable to use since it would cover the combined more significant portion of population
distribution compared to using the mean and standard deviation in the calculation of the interval.
Question 3
Part D
From the data, the heart rate that represents men is 73.4 while for women is 74.2. The
values are the mean scores for the heart bit rates preferred for representation since they indicate
the average scores for the entire samples.
Part E
The data for the female has more variability compared to that for male due to a more
significant divergence from the average or the mean as indicated by the variance and the
standard deviation
Part F
The interval for the normal heart rates based on quartiles is 68 – 80 for female while 70-
78 for male. The use of quartiles was preferred due to a broad distribution of the population
covered with the range compared when calculated using mean and the standard deviation.
Part G
Based on this statistic, the nurses should use the quartiles for intervals of typical heart
rates for adults with different ranges for men and women since both the gender exhibit different
heart rates in nature, as indicated by the data.