HW 5
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Seton Hall University *
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1203
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Mathematics
Date
Jan 9, 2024
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3
Uploaded by marielgar42
MATH 1203
H
OMEWORK
#5
M
ARIEL
G
ARCIA
Please answer all of the following questions and show all your work:
1) Projecting ahead to 2100, the population in New Jersey counties is expected to
increase/decrease by the following amounts (in 1000s):
30, -5.5, 13.7, 7.5, 4.6, 23.3, -2.3, 42.4, 4.8, 13.5, 3.3, -3.7, -2.6, 12.4, 7.9, 23.7, 3, 41,
-3.4, 13.9, 3.5
What are the Median and Mode(s) for the changes for these 21 counties? Compared
to the Mean (11.0), what would we say about the Skew of the Sample?
-5.5, -3.7, -3.4, -2.6, -2.3, 3, 3.3, 3.5, 4.6, 4.8, 7.5, 7.9, 12.4, 13.5, 13.7, 13.9, 23.3, 23.7,
30, 41, 42.4
The Median is 7.5. There is no Mode. The Mean is 11 (add all numbers together, then
divide by the amount). Due to the median being less than the mean, the skew of the
sample would result in being to the right.
2) The price of Gold per ounce had the following values over a 7-day period:
$1637, 1718, 1704, 1686, 1698, 1690, 1704
What were the Median and Mode prices of Gold for this week? Comparing the
Median to the Mean (1691), what would we say about the Skew of the Sample?
1637, 1686, 1690, 1698, 1704, 1704, 1718
The median is 1698. The mode is 1704. The mean is 1691 (add all numbers together,
then divide by the amount). Due to the mean being less than the median, the skew of
the sample would result in being to the left.
3) In the US census data for 2021, full-time Median income for women was $52,979
and Mean income was $71,253. For men, the Median was $63,743 and the Mean was
$92,094.
a) Are one or both of these income distributions Skewed? If so, which way?
Both of these income distributions are skewed. Due to the women’s income median
being less than the mean income, it would skew to the right. Due to the mens income
median being less than the mean income, it would also skew to the right.
b) We often say “US women earn 80¢ for every 1 dollar made by a US man”. Which
statistic (Mean, Median) gives us that conclusion? And why do we use that statistic
and not the other one for calculating women’s pay in relation to men’s pay?
The statistic that gives us this conclusion is the mean. We use this statistic and not
the other because the mean is practically the average and realects changes in values.
The median is just the center, and would not give us the necessary information for
this issue.
4) A Federal Reserve study of household income showed between 1989 and 2013,
the Median family net worth changed from $85,060 to $81,400, but their Mean net
worth rose from $342,300 to $528,420. How could the Median go down if the Mean
is going up?
The median could go down if the mean is going up when there are a lot more values
in the data. The more values, the lower the median may get since it is the center. The
mean would increase due to this increase of values.
5) Our study on the farmers’ markets and organic produce growers gave us the
following Frequency Table.
a) Fill out the Frequency Table for the study, and use it to aind the Mean, Median, and
Mode:
Mean- 0(22)+1(18)+2(14)+3(20)+4(22)+5(4)
—————————————————-
= 2.14
(22+18+14+20+22+4)
Median- (14+20)/2 = 17
Mode- 22
b) Does there appear to be any Skew in our Sample? Why or why not?
There appears to be a skew to the left. This is because the mean is less than the
median.
6) [StatCrunch] For the Student Survey data aile, can we calculate Mean, Median, or
Mode for Religious Observance (“Relig”)? If so, what are the values? Should we use
them? What about for Belief in Life after Death (“Life”)?
Number of
Organic growers:
0
1
2
3
4
5
total
Frequency:
22
18
14
20
22
4
100
Rel. Frequency:
0.22
0.18
0.14
0.20
0.22
0.04
1
Cum. Rel. Freq:
0.00220.0018
0.0014
0.0020
0.0022
0.0004
Yes we can calculate the mean, median, and mode. The mode is 1. The mean is
1.1667. The median is 1. We shouldn’t use them since the three values are very
similar and there would not be much of a skew in the data. For belief in life after
death, the mode is y. The median and mean are not able to be calculated since they
are not real values.
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