Question

Depth: μ= ____ ​km ; M=_____ km; Range=______km ; σ=______ km ; Q1=_____​km ; Q3=_____km

Magnitude: μ=_______​; M=______​; R=_______​; σ=________​; Q1=_______; Q3=________

Conjecture the shape of the distribution for depth. Choose the correct answer below.

OPTION A.The mean is much larger than the median and is greater thanQ3​, so the distribution of depth is likely skewed left.

OPTION B.The mean is much smaller than the median and is less than Q1​, so the distribution of depth is likely skewed left.

OPTION C.The mean is much larger than the median and is greater than Q3​, so the distribution of depth is likely skewed right.

OPTION D.The mean is close to the​ median, and the distance from Q1 to the median is close to the distance from Q3 to the​ median, suggesting the distribution of depth is approximately symmetric.

Conjecture the shape of the distribution for magnitude. Choose the correct answer below.

OPTION A.The mean is larger than the​ median, and the distance from Q1 to M is less than the distance from M to Q3​, which suggests the distribution of magnitude is skewed right.

OPTION B.The mean is close to the​ median, and the distance from Q1 to the median is close to the distance from Q3 to the​ median, suggesting the distribution of magnitude is approximately symmetric.

OPTION C.The mean is smaller than the​ median, and the distance from M to Q3 is less than the distance from Q1 to​ M, which suggests the distribution of magnitude is skewed left.

OPTION D.The mean is smaller than the​ median, and the distance from M toQ3 is less than the distance from Q1 to​ M, which suggests the distribution of magnitude is skewed right.

b) Draw a relative frequency histogram for both depth and magnitude. Label the mean and median on the histogram. Describe the shape of each histogram.

Draw a frequency histogram below for magnitude.

Describe the shape of each histogram. Choose the correct answer below.

OPTION A.The histogram for depth is skewed​ left, whereas the histogram for magnitude is skewed right.

OPTION B.The histograms for both depth and magnitude show skewed right distributions. The skewness is more defined for depth.

OPTION C.The histogram for depth is skewed​ right, whereas the histogram for magnitude is skewed left.

OPTION D. The histograms for both depth and magnitude show skewed left distributions. The skewness is more defined for magnitude.

(c) Draw a boxplot for both depth and magnitude. Are there​ outliers?

Draw a boxplot below for magnitude.

Are there​ outliers?

OPTION A. ​Yes; the boxplots for both depth and magnitude show outliers.

OPTION B. Yes; the boxplot for depth shows outliers. There are no outliers for magnitude.

OPTION C. ​No; there are no outliers for either variable.

OPTION D. Yes; the boxplot for magnitude shows outliers. There are no outliers for depth.

​(d) Determine the lower and upper fences for identifying outliers for both depth and magnitude.

Depth: Lower fence:______ ;; Upper fence:_____

​Magnitude: Lower fence:______ ;; Upper fence:_____

depth   magnitude
2.24   0.57
1.78   0.99
1.1   1.52
7.46   2.49
2.3   1.36
9.27   0.35
8.06   1.34
2.37   0.75
8.83   0.8
5.09   2.39
8.54   0.56
3.04   2.7
0   1.92
5.81   1.69
127.91   3.29
2.21   1.33
16.08   2
1.58   1.1
12.21   1.27
114.39   4.38
23.29   4.3
9.63   0.05
6.44   0.62
14.76   1.3
3.8   1.65
2.46   0.83
2.59   0.94
19.85   6.64
18.29   1.6
10.86   1.57
17.48   1.12
19.99   0.69
15.67   0.64
8.55   1.59
16.63   0.67
508.65   4.28
130.78   2.38
7.37   1.97
2.51   0.43
7.02   0.98
2.91   2.41
2.07   1.03
211.2   2.88
10.82   1.91
35.16   1.69
0.03   1.42
8.51   1.07
17.22   1.1
3.42   0.61
7.01   1.34
1.83   0.59
44.85   3.37
6.04   0.92
2.25   0.52
2.06   2.71
1.17   1.63
3.01   0.87
75.85   1.51
1.92   1.15
2.22   1.12
0.19   0.39
0.74   0.84
4.96   0.47
8.16   0.35
33.84   1.33
21.44   1.6
35.13   4.61
10.07   5.48
48.4   1.99
10.58   1.27
14.83   1.39
6.23   0.93
6.4   0.9
99.18   3.43
4.16   0.67
9.38   1.58
9.45   0.97
0.01   1.17
6.51   5.1
14.12   1.39
6.35   0.77
349.98   5.02
1.8   1.8
6.45   1.04
138.4   4.27
5.89   1.4
6.8   0.1
13.21   0
10.85   0.89
18.35   0.89
7.32   1.64
0   1.05
0   1.02
22.81   1.2
6.87   1.3
16.35   1.15
2.25   1.28
4.72   2.59
4.57   1.55
2.59   0.78

Answer 1

Solution:

Perfomed in Rstudio

Rcode:

DF=read.table(header = TRUE, text ="
depth magnitude
2.24 0.57
1.78 0.99
1.1 1.52
7.46 2.49
2.3 1.36
9.27 0.35
8.06 1.34
2.37 0.75
8.83 0.8
5.09 2.39
8.54 0.56
3.04 2.7
0 1.92
5.81 1.69
127.91 3.29
2.21 1.33
16.08 2
1.58 1.1
12.21 1.27
114.39 4.38
23.29 4.3
9.63 0.05
6.44 0.62
14.76 1.3
3.8 1.65
2.46 0.83
2.59 0.94
19.85 6.64
18.29 1.6
10.86 1.57
17.48 1.12
19.99 0.69
15.67 0.64
8.55 1.59
16.63 0.67
508.65 4.28
130.78 2.38
7.37 1.97
2.51 0.43
7.02 0.98
2.91 2.41
2.07 1.03
211.2 2.88
10.82 1.91
35.16 1.69
0.03 1.42
8.51 1.07
17.22 1.1
3.42 0.61
7.01 1.34
1.83 0.59
44.85 3.37
6.04 0.92
2.25 0.52
2.06 2.71
1.17 1.63
3.01 0.87
75.85 1.51
1.92 1.15
2.22 1.12
0.19 0.39
0.74 0.84
4.96 0.47
8.16 0.35
33.84 1.33
21.44 1.6
35.13 4.61
10.07 5.48
48.4 1.99
10.58 1.27
14.83 1.39
6.23 0.93
6.4 0.9
99.18 3.43
4.16 0.67
9.38 1.58
9.45 0.97
0.01 1.17
6.51 5.1
14.12 1.39
6.35 0.77
349.98 5.02
1.8 1.8
6.45 1.04
138.4 4.27
5.89 1.4
6.8 0.1
13.21 0
10.85 0.89
18.35 0.89
7.32 1.64
0 1.05
0 1.02
22.81 1.2
6.87 1.3
16.35 1.15
2.25 1.28
4.72 2.59
4.57 1.55
2.59 0.78

"
  
)
DF
summary(DF)
fivenum(DF$depth)
sd(DF$depth)
median(DF$depth)
mean(DF$depth)
range(DF$depth)   
fivenum(DF$magnitude)
sd(DF$magnitude)
median(DF$magnitude)
mean(DF$magnitude)
range(DF$magnitude)
Output:

To get relative histograms RcodeL

library(lattice)
histogram(DF$depth,xlab="Depth",main="Relative Histogram")
histogram(DF$magnitude,xlab="magnitude",main="Relative Histogram")

To get boxplot:

boxplot(DF$depth,xlab="Depth",main="Boxplot",horizontal = TRUE,col="blue")
boxplot(DF$magnitude,xlab="Magnitude",main="Boxplot",horizontal = TRUE,col="blue")

Depth: μ= 25.9578 ​km ; M=7.17km; Range=508.65 km ; σ=67.83865 km ; Q1=2.550​km ; Q3=16.215km

Magnitude: μ=1.625​; M=1.29​; R=6.64​; σ=1.261018​; Q1=0.880; Q3=1.855

OPTION C.The mean is much larger than the median and is greater than Q3​, so the distribution of depth is likely skewed right

OPTION B.The histograms for both depth and magnitude show skewed right distributions. The skewness is more defined for depth.

OPTION A. ​Yes; the boxplots for both depth and magnitude show outliers.