Mathematics Assignment
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Mathematics Assignment
Student Name:
Instructor Name:
Course Number:
20th May 2019
Student Name:
Instructor Name:
Course Number:
20th May 2019
Question 2
Part a
i)
ii) This is a continuous data.
iii) From the above table, the two measures of location that we do have are median and
mean. Using mean, then men have greater salary on average (31.7 thousands of pounds)
compared to women who have salary of 27.1 thousands of pounds. On the other hand
when median is used we still find that the same men have greater salary on average (32
thousands of pounds) compared to women’s 26.5 thousands of pounds.
iv) From this table, the three measures of spread that we have are range, inter quartile range
and standard deviation. Considering the range of women’s salary (11 thousands of
pounds) versus men’s salary (10 thousands of pounds) we find that women’s salary has
a greater variability than those of men. The standard deviation for women salary (3.5
thousands of pounds) also has a greater variability compared to standard deviation of
men’s salary of 3.0 thousands of pounds. Lastly the inter quartile range for women’s
salary (6 thousands of pounds) also shows a greater variability than men’s 3 thousands
of pounds. In conclusion having looked at the three measures of spread we can say that
women’s salary showed greater variability compared to men’s.
Women’s salaries
(thousands of pounds)
Men’s salaries
(thousands of pounds)
Min 22 26
median 26.5 32
max 33 36
Mean 27.1 31.7
SD 3.5 3.0
IQ range 6 3
Range 11 10
Part a
i)
ii) This is a continuous data.
iii) From the above table, the two measures of location that we do have are median and
mean. Using mean, then men have greater salary on average (31.7 thousands of pounds)
compared to women who have salary of 27.1 thousands of pounds. On the other hand
when median is used we still find that the same men have greater salary on average (32
thousands of pounds) compared to women’s 26.5 thousands of pounds.
iv) From this table, the three measures of spread that we have are range, inter quartile range
and standard deviation. Considering the range of women’s salary (11 thousands of
pounds) versus men’s salary (10 thousands of pounds) we find that women’s salary has
a greater variability than those of men. The standard deviation for women salary (3.5
thousands of pounds) also has a greater variability compared to standard deviation of
men’s salary of 3.0 thousands of pounds. Lastly the inter quartile range for women’s
salary (6 thousands of pounds) also shows a greater variability than men’s 3 thousands
of pounds. In conclusion having looked at the three measures of spread we can say that
women’s salary showed greater variability compared to men’s.
Women’s salaries
(thousands of pounds)
Men’s salaries
(thousands of pounds)
Min 22 26
median 26.5 32
max 33 36
Mean 27.1 31.7
SD 3.5 3.0
IQ range 6 3
Range 11 10
Part b
i)
ii) The data is right skewed (positively skewed). This is due to the fact that the mean (27.1
thousands of pounds) is greater than the median (26.5 thousands of pounds).Besides
this we find that the median (26.5 thousands of pounds) is closer to the first quartile
(24 thousands of pounds) than the third quartile (30 thousands of pound)) hence
making the tail of distribution on the right hand sides to be longer than the one on left
hand side.
iii)
(1) The statement is false. From the box plot it is evident that about twenty five percent
of women are paid less than £ 24000.
(2) The statement is false. The men paid more than 32 thousands of pounds are about
40% while the Men paid less than 32 thousands of pounds are about 45%. Therefore
we can say that there are less men paid more than 32 thousands of pounds as compared
to those paid less than 32 thousands of pounds.
i)
ii) The data is right skewed (positively skewed). This is due to the fact that the mean (27.1
thousands of pounds) is greater than the median (26.5 thousands of pounds).Besides
this we find that the median (26.5 thousands of pounds) is closer to the first quartile
(24 thousands of pounds) than the third quartile (30 thousands of pound)) hence
making the tail of distribution on the right hand sides to be longer than the one on left
hand side.
iii)
(1) The statement is false. From the box plot it is evident that about twenty five percent
of women are paid less than £ 24000.
(2) The statement is false. The men paid more than 32 thousands of pounds are about
40% while the Men paid less than 32 thousands of pounds are about 45%. Therefore
we can say that there are less men paid more than 32 thousands of pounds as compared
to those paid less than 32 thousands of pounds.
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