Assiut University
Multivariate Statistics
Faculty of Engineering
Eelective Course (3)
Mining Engineering Department
4th Year Mining Engineering
Final Exam: June 2003
Time Allowed: 3 Hours
Attempt all the following questions
1. What are the main three categories required for summary statistics of earth science data
sets? Write the equations when necessary.
(9 marks)
2.
Table (1): Lead grades (%) measured in 2 m long drill core segments.
marks)
9.24 6.27 5.1
1.1
1.18 1.04 1.02 4.69 7.16
1.58 1.48 1.03 1.66 5.40 2.38 0.81 0.50 1.12
3.77 6.71 3.82 4.345 3.26 4.12
(15
9.25
1.60
You are required to:
a- Determine the summary statistics of the Pb grades.
b- Calculate the sample variance, the standard deviation and the coefficient of
variation for the given data.
c- Draw the Histogram and probability plot of the Pb grades.
3.a.
3.b.
4.
Explain when and why we use the following:
(6 marks)
Correlation coefficient – PCA – FA
The data for multivariate analysis should always be examined and tested for
Normality, and Homogeneity of variances.
(6 marks)
i.
Why? Give reasons
ii.
Explain with sketches two methods to assess the normality of the
variables.
Use the Triangle Method to calculate the average thickness and the total ore
reserve in tons for the region shown in the Figure below. Sampling data are
given in Table (2). Assume that the ore density = 1.428 t/m3
(24 marks)
M5
M6
M2
M3
M4
M1
Table (2): X, Y co-ordinates and the thickness of the sampling boreholes.
B.H. X, (m)
Y, (m)
t, (m)
Side
L, (m)
B.H.
M1
2698.53
542.73
4
6
M2
2838.18
1749
5.2
M3
2143.41
1147.79
Area of Triangle M3-M4-M6 = 289569.94 m2
Area of Triangle M3-M4-M1 = 206700.86 m2
t, (m)
7
4.5
3.6
M2-M5
698.345
M4
M3-M5 1351.529
M5
M5-M6 1381.228
M6
Periphery of Triangle M3-M5-M6
= 4374.48 m
Good Luck
Dr. SaMeH Saadeldin + the committee