.1. Earthquake records. Measurements of engineering interest have been recordedduring earthquakes in Japan and in other parts of the world since 1800. Oneof the critical recordings is of apparent relative density, RDEN. After the com-mencement of a strong earthquake, a saturated fine, loose sand undergoes vibra-tory motion and consequently the sand may liquefy without retaining any shearstrength, thus behaving like a dense liquid. This will lead to failures in structuressupported by the liquefied sand. These are often catastrophic. The standard pen-etration test is used to measure RDEN. Another measurement taken to estimatethe prospect of liquefaction is that of the intensity at which the ground shakes.This is the peak surface acceleration of the soil during the earthquake, ACCEL.The data are from J. T. Christian and W. F. Swiger (1975), J. Geotech. Eng. Div.,Proc. ASCE, 101, GT111, 1135–1150, and are reproduced by permission of thepublisher (ASCE):RDEN ACCELRDEN ACCELRDEN ACCEL(%)(units of g)(%)(units of g)(%)(units of g)530.219300.138500.313640.219720.422440.224530.146900.5561000.231640.146400.447650.334650.684500.547680.419550.611550.204780.352750.591500.170580.363720.522550.170800.291400.258750.192550.314580.250530.2921000.377430.283700.2991000.434320.419640.292520.350400.123530.225580.334| Note: g denotes acceleration due to gravity (9.81 m/s²).Compute the sample mean x, standard deviation §, and the coefficient of skewness,81, for RDEN and ACCEL. Construct stem-and-leaf plots for each set. Comment onthe distributions. Plot the scatter diagram and calculate the correlation coefficientr. What conclusions can be reached?

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Description: .1. Earthquake records. Measurements of engineering interest have been recordedduring earthquakes in Japan and in other parts of the world since 1800. Oneof the critical recordings is of apparent relative density, RDEN. After the com-mencement of a

Mean: Mean is defined as the sum of observations divided by the number of observations. Mean(x bar)…

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Statistics

Compute the sample mean , standard deviation §, and the coefficient of skewness, g1, for RDEN and ACCEL. Construct stem-and-leaf plots for each set. Comment on the distributions. Plot the scatter diagram and calculate the correlation coefficient r. What conclusions can be reached?

Compute the sample mean , standard deviation §, and the coefficient of skewness, g1, for RDEN and ACCEL. Construct stem-and-leaf plots for each set. Comment on the distributions. Plot the scatter diagram and calculate the correlation coefficient r. What conclusions can be reached?

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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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Question

.1. Earthquake records. Measurements of engineering interest have been recorded
during earthquakes in Japan and in other parts of the world since 1800. One
of the critical recordings is of apparent relative density, RDEN. After the com-
mencement of a strong earthquake, a saturated fine, loose sand undergoes vibra-
tory motion and consequently the sand may liquefy without retaining any shear
strength, thus behaving like a dense liquid. This will lead to failures in structures
supported by the liquefied sand. These are often catastrophic. The standard pen-
etration test is used to measure RDEN. Another measurement taken to estimate
the prospect of liquefaction is that of the intensity at which the ground shakes.
This is the peak surface acceleration of the soil during the earthquake, ACCEL.
The data are from J. T. Christian and W. F. Swiger (1975), J. Geotech. Eng. Div.,
Proc. ASCE, 101, GT111, 1135–1150, and are reproduced by permission of the
publisher (ASCE):
RDEN ACCEL
RDEN ACCEL
RDEN ACCEL
(%)
(units of g)
(%)
(units of g)
(%)
(units of g)
53
0.219
30
0.138
50
0.313
64
0.219
72
0.422
44
0.224
53
0.146
90
0.556
100
0.231
64
0.146
40
0.447
65
0.334
65
0.684
50
0.547
68
0.419
55
0.611
55
0.204
78
0.352
75
0.591
50
0.170
58
0.363
72
0.522
55
0.170
80
0.291
40
0.258
75
0.192
55
0.314
58
0.250
53
0.292
100
0.377
43
0.283
70
0.299
100
0.434
32
0.419
64
0.292
52
0.350
40
0.123
53
0.225
58
0.334
| Note: g denotes acceleration due to gravity (9.81 m/s²).
Compute the sample mean x, standard deviation §, and the coefficient of skewness,
81, for RDEN and ACCEL. Construct stem-and-leaf plots for each set. Comment on
the distributions. Plot the scatter diagram and calculate the correlation coefficient
r. What conclusions can be reached?

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