Basic Statistics and introductory probability theory, Semester 1(2020-23), First Internal Feb 2021
BASIC STATISTICS
AND INTRODUCTORY PROBABILITY THEORY
Total : 50
marks Time: 2 hours
Section
A
Answer any 5
questions. Each question carries 2 marks.
1. statistics should be an aggregate of facts,
numerically expressed, collected in systematic manner, collected for
predetermined purposes, simplify complexity
2. AM can be easily calculated; it can be
determined in most of the cases.it is based on all observations of the data.
Thus, mean satisfies many of the properties of a good average. That is why
arithmetic mean is considered to be the best average.
3. Correlation is the relationship between two or
more variables.
Eg:
Relation between demand and supply
4. Regression is the prediction of the unknown
variable’s value from known variable’s value
5. probable error of the coefficient of
correlation is a statistical measure which measures reliability and
dependability of the value of coefficient of correlation
Or
P.E= 0.6745(1-r2)/sqrt(n)
6. 3x+2y+4=0
3x=
-2y-4
x =
-0.67y-1.33, bxy=-0.67
or -2/3
Section
B
Answer any 5 questions.
Each question carries 5 marks.
7. n1 =22, n2= 18,
Combined
mean=22x15+18x20/22+18=17.25
8. properties of correlation coefficient-it has a well-defined
formula, it is independent of the unit of measurement, it lies between -1 and 1,
it does not change with reference to change of origin
Difference between correlation and regression-1) in correlation, we
study degree of relationship between the variables.in regression analysis-we study
the nature of relationship 2) in correlation analysis, the choice of dependent
and independent variables is purely personal choice, in regression analysis,
one has to decide which variable shall be taken as dependent and which as
independent
3) correlation is not for prediction and regression is used for
prediction
9.
|
X |
5 |
8 |
7 |
11 |
9 |
10 |
8 |
2 |
4 |
6 |
|
X2 |
25 |
64 |
49 |
121 |
81 |
100 |
64 |
4 |
16 |
36 |
S.D=sqrt(560/10-(70/10)2=sqrt(56-49=sqrt(7)=2.646
10.r=0.2
1-0.02=6∑ D2/n
(n2-1)
∑D2 =792/6=132, correct
∑D2 =132-49+81=164
There fore correct correlation
coefficient=1-0.99=0.01
11.
|
x |
y |
xy |
Y2 |
|
5 |
4 |
20 |
16 |
|
6 |
5 |
30 |
25 |
|
7 |
8 |
56 |
64 |
|
3 |
2 |
6 |
4 |
|
2 |
1 |
2 |
1 |
|
23 |
20 |
114 |
110 |
bxy=0.73, mean of x=4.6, mean of y=4
Regression equation of x on y
is x-4.6=0.73(y-4)
X=0.73y+1.68
12.
|
x |
1/x |
f |
f/x |
|
60 |
0.016 |
600 |
10 |
|
15 |
0.0667 |
300 |
20 |
|
350 |
0.0029 |
700 |
2 |
|
50 |
0.0200 |
25 |
0.5 |
Average speed=N/∑ f(1/x)= 1625/32.5=50K.M p.h
Section
C
Answer any 1 question.
It carries 15 marks.
13. mean=33.71,median=33.5 and mode=33.85,and draw less than ogive by
writing less than cumulative frequency
14. Karl Pearson’s correlation coefficient=
35770-37045/sqrt(24850-24025)*(53250-57121)
=-1275/1325.2=-0.962=negative correlation
byx =1.5,mean of x=4,mean of y=5.8,y=1.5x-0.2
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