The prediction of student success in the study of elementary business statistics

160 Pages·05.471 MB·English

by  Roberts, James Harold, Jr

THE PREDICTION OF STUDENT SUCCESS IN THE STUDY OF
ELEMENTARY BUSINESS STATISTICS
A Thesis
Presented to
the F aculty of the School o f Commerce
U n iversity o f Southern C aliforn ia
In P a rtia l F ulfillm ent
o f the Requirements for the Degree
M aster of B usiness A dm inistration
by
James Harold R oberts, Jr
August 1950
UMI Number: EP43309
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This thesis, ‘written by
JME3_MR0LD_.^BEHT3.a..JR.,
under the guidance of h..XSi. Faculty Committee,
and approved by all its members, has been
presented to and accepted by the Council on
Graduate Study and Research in partial fulfill­
ment of the requirements for the degree of
MASTER OF BUSINESS ADMINISTRATION
AUG 195Q.
Date...
Faculty Committee
Chairman
i
TABLE OF CONTENTS
CHAPTER PAGE
I . THE PROBLEM AND PROCEDURE OF THE STUDY . . . . 1
The problem ........................................................................ 1
Statement of the problem ......................... 1
Importance of the study ......................... 1
D elim itation s o f the study . .......................... 2
D efin ition s o f terms . . . . . . . . . . . . 3
S ta tistic s . . . . . . . . . . .......................... 3
Elementary business s t a t i s t i c s ......................... 3
Procedure o f the s tu d y ............................................. . 3
s. O rganization o f the s t u d y ......................... A
II. THE PREDICTION OF SCHOLASTIC ACHIEVEMENT . . . 5
P rognosticating achievement in the foreign
languages 5
A study o f the p red ictive values o f certain
te s t elem ents for freshman chem istry • * 6
-Prediction equation for su ccess in co lleg e
mathematics ......................... ?
Summary . . . . . . . . . . . . . . . . . 8
II I. THE COURSE OF STUDY .......................... 9
S election of tex ts . . . . . . . 9
Method of tabulation ......................... 10
Typical course o f study .......................... 11
l i
CHAPTER PACE
IV. MATHEMATICS USER IN THE COMPUTATION OF THE
MEASURES OF CENTRAL TENDENCY . . . . . . . . 13
A rithm etic mean ......................... 13
The arithm etic mean from ungrouped data . 13
The arithm etic mean from grouped data . . 1^
M athematics used to compute th e arithm e-
t ic mean . ........................................................ 16
Median • « . » » » * • » ■ » . . . . . . . . . 16
The median from ungrouped data ..................... 16
The median from grouped d a t a ............................. 17
M athematics used to compute the median . . 18
The mode .................................................................................. 18
The mode from ungrouped d a t a ............................. 18
The mode from grouped d a t a .................................. 18
Mathematics used in the computation of the
mode . . * ......................... . 19
The geom etric mean . . . . . . . . . . . . . 19
Geometric mean from ungrouped data . . . . 20
Geometric mean from grouped data . . . . . 21
M athematics used in the computation o f the
geom etric mean . . . . . . . . . . . . . 21
The harmonic m e a n ......................................... 22
The harmonic mean from ungrouped data . . 22
The harmonic mean from grouped data . . . 23
i l l
CHAPTER PAGE
M athematics used in the computation of
the harmonic m e a n .......................... . . . . . 23
M athematics used in the com putations o f
measures of cen tral ten d en cy ......................... . 24
V. MATHEMATICS USED IN THE COMPUTATION OF THE
Measurement of absolute disp ersion —the
range . . . . . . . . . . . . . ..................... 26
Measurement o f absolute d ispersion— q u artlie
d eviation . . . . . . . . . . . 26
Q uartlle d eviation o f ungrouped data . . . .2 ?
Q uartlie deviation o f grouped data . . . . 28
M athematics used In the computation of the
q u artlle deviation ............................................... 29
Measurement o f absolute d isp ersion — average
d e v ia t io n ................................... 29
Average .deviation from ungrouped data . . 30
Average d eviation from grouped data . . . 31
M athematics used in the computation of the
average d e v ia t io n ......................... 3k
Measurement o f absolute d isp ersion — standard
d eviation . . . . . . . . . . . . . . . . 3k
The standard d eviation from ungrouped
data ................................... 34
Standard d eviation from grouped data . . . 35
iv
CHAPTER PAGE
M athematics used in the computation of
the standard d e v ia tio n .......................................... 37
Measurement o f r e la tiv e disp ersion —
c o e ffic ie n t o f variation ......................... 38
M athematics used in the computation o f the
c o e ffic ie n t o f v a r ia tio n ..................................... 39
Measurement o f r e la tiv e d isp ersion —
c o e ffic ie n t o f skewness ..................................... 39
M athematics used in the computation o f the
co e ffic ie n t o f skewness . . . . . . . . 40
M athematics used in the com putations of the
measures of d isp ersion . . . . . . . . . . 41
VI. MATHEMATICS USED IN THE COMPUTATION AND
APPLICATION OF LINEAR CORRELATION..................... 42
C orrelation—rank d ifferen ce method . . . . 43
M athematics used in the computation of the
c o efficien t o f correlation — rank
d ifferen ce method . . . . . .......................... 44
C orrelation—product moment method . . . . . 45
Product moment method—ungrouped data . . 45
Product moment method—grouped data . . . 47
M athematics used in the com putation"of the
c o efficien t o f co rrela t ion— product
moment method 49
V
CHAPTER PAGE
A pplication of lin ea r correlation — the
regression equation .................................................... 50
M athematics used in the computation o f the
regression equation . . . . .......................... 52
M athematics used in the com putation and
ap p lication o f lin ea r correlation . . . . 52
Y II. MATHEMATICS USED IN THE COMPUTATION OF THE
MEASURES OF RELIABILITY AND SAMPLING . . . . 53
Standard error of the mean ..................................... 5^
Probable error.of the mean . . . . . . . . . 55
Standard error o f correlation . . . . . . . 56
Probable error o f correlation • ..................... 57
Standard error of e stim a te ...............................1, . 57
Standard error of the d ifferen ce between two
m e a n s ......................................................................... 59
M athematics used in the computation o f the
measures o f r e lia b ility and sam pling . . . 61
V III. MATHEMATICS USED IN THE ANALYSIS OF TIME
SERIES ............................................................................. 63
Secular trend .................................................... 6k
Secular trend - free hand in sp ection . . . 6k
Secular trend - method of sem i-averages . 6k
Secular trend - method o f moving averages 65
Secular trend - method of le a s t squares . 66
Vi
CHAPTER PAGE
M athematics used in the ca lu la tio n of
secu lar trends .............................................................. 72
Seasonal variation . . . . . . . . ..................... 72
Index o f seasonal variation — sim ple
average method . . . . . . . . . . . . . 73
Index o f seasonal variation — ra tio s to
moving average method .......................................... 76
M athematics used in the calcu lation of
seasonal variation .................................................... 79
C yclical flu ctu ation . . . . . . . . . . . . 79
M athematics used in the calcu lation of
c y c lic a l flu ctu a tio n ............................................... 81
M athematics used in the an alysis of time
se r ie s ......................... 81
IX. MATHEMATICS USED IN THE CONSTRUCTION OF INDEX
NUMBERS ........................................ 82
Priee index ........................................................................ 82
Simple aggregative price index . . . . . . 83
Simple average o f r ela tiv e s p rice index . 83
W eighted average o f r ela tiv e s p rice index 8k
W eighted aggregative price index ..................... 86
Q uantity index . . . . . . . . . . . . . . . 87
Sim ple aggregative quantity index . . . . 87
v ii
CHAPTER PAGE
W eighted average o f rela tiv e s quantity
index ........................................ 89
W eighted aggregative quantity index . . . 90
M athematics used in the construction of
index numbers . . . . . . ..................................... 91
X. THE TEST . ................................................... 92
Test construction ......................................................... 92
Method ........................................................................................ 94
The experim ental group . . . . . . . . . . 94
A dm inistration o f the t e s t ..................................... 94
Sample . . . . . . . . . . . . . . . . . . . 94
The sample as rep resen tative o f a college
population . . . . . . . . . . ..................... 94
R e lia b ility and scoring . . . . . . . . . . 95
XI. RESULTS AND INTERPRETATION ......................... 97
X II. SUMMARY AND CONCLUSIONS.................................... 99
Summary ....................................................................... 99
Conclusions . . . . . . . . . . . . . . . . 100
BIBLIOGRAPHY . . . . . . . ............................................................. 102
APPENDIX A. Composite Tabulation o f Subject M atter 104
APPENDIX B. M athematics T e s t .................................... 107
APPENDIX C. R e lia b ility o f the M athematics Test . . 114
APPENDIX D. Adjusted M athematics Test . . . . . . . 130
APPENDIX E. R esults of Individual P redictions . . . 135