HW 6
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Seton Hall University *
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1203
Subject
Mathematics
Date
Jan 9, 2024
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Uploaded by marielgar42
MATH 1203
H
OMEWORK
#6
M
ARIEL
G
ARCIA
Please answer all of the following questions and show all your work:
1) The price of Gold per ounce had the following values over a 7-day period:
$1637, 1718, 1704, 1698, 1686, 1690, 1704
What is the Range for the sample? What is the Variance, s
2
, and the Standard
Deviation, s, given that the Mean is 1691?
- The range for the sample is (1718 - 1637) 81. The variance is
(1637+1718+1704+1698+1686+1690+1704/7 = 1691 (subtract each point from
mean value and square each) 2916 + 729 + 169 + 49 + 25 + 1 + 169 = 4058/7-1)
676.33. The standard deviation is (square root of variance) 26.01.
2) [StatCrunch] Compare the Hours Watching Television (“TV”) and Hours Playing
Sports/Exercising (“Sport”) Ranges and Standard Deviations. Which Variable shows
more Variability? What value would we need to be 1 “step” below and 1 “step”
above the Mean for TV? For Sports?
The range for the Hours Watching Television is (37-0) 37, while the range for Hours
Playing Sports/Exercising is (15-0) 15. The range for TV is much greater. The
standard deviation for TV is 6.71 while for Sport it is 3.87. Once again, the TV is
greater than Sport. The variability for TV shows more variability because the
standard deviation is greater.
3) Projecting ahead to 2100, the population in New Jersey counties is expected to
increase/decrease by the following amounts:
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
The Mean,
, for the Sample is 11.0. Is the measurement of -2.6 “farther away” from
the center of this Sample than the measurement of 1704 is from the center of the
Sample in Question 1? (Hint: What are the z-scores for each measurement?)
-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 center of this sample is 7.7. This means that the measurement, 11, is not -2.6
“farther away” of this sample than the measurement of 1704 from the center of the
sample in question 1.
¯x
4) For our IQ measurement Sample, we get an additional score of 180, giving us:
{100, 115, 96, 88, 117, 160, 120, 72, 130, 102, 180}
Create a 5-Number Summary and calculate the IQR. Are there any Outliers in the
expanded Sample? Why or why not?
72, 88, 96, 100, 102, 115, 117, 120, 130, 160, 180
Min: 72
Q1: 96
Q2 (median): 115
Q3: 130
Max: 180
IQR: 34
- There are no outliers. This is because the numbers are all in range.
5) [StatCrunch] For the Student Survey, create Box Plots for High School GPA
(HSGPA) and College GPA (COGPA). Which one shows more Variability? Does either
show Skew?
- The college gpa shows more variability. The taller the box, it implies more variable
data. The high school gpa shows a slight left skew. The college gpa shows a slight left
skew as well.
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