SECTION - A
QUESTION 1
(a) A saving account opened 3 months ago now has a balance of Rs. 2,040. If
the bank pays 8% simple interest, how much money was deposited?

A = 2,040, r = 8%, n = 3/12 = ¼ year
A = P + S.I = P + P x r x n
100
A = P 1 + r.n
P= A
100
1 + r.n
100
P = 2040
= 2040 = 2040
1 + 8 x 0.25 1 + 0.02
1.02
100
= Rs. 2,000
Commodity
Base period
Current Period
Price
Total value
Price
Total Value
A
5
60
6
60
B
6
48
7
105
C
4
68
5
100
D
7
105
8
96
E
8
96
9
135
Commo
dity
p○
5
12
6
10
60
72
50
60
6
8
7
15
48
56
90
105
4
17
5
20
68
85
80
100
7
15
8
12
105
120
84
96
8
12
9
15
96
108
120
135
377
441
424
496
QUES. 1 (D): FIND MEDIAN
Mid-value
5
15
25
35
45
55
65
75
Frequency
15
7
11
10
13
8
20
16
Classes
f
c.f.
0-10
15
15
10-20
7
22
20-30
11
33
30-40
10
43 (c.f.)
40-50
13 (f)
56 M
50-60
8
64
60-70
20
84
70-80
16
100
N = 100
Since, we are given the mid-values, we
should first find out the upper and lower
limits of the various classes. Thus, the
class intervals of the mid-values are
obtained.
Median = Size of {N/2}th item = 100/2 =
50th item
Therefore, Median lies in the class 40—50
M = l + N/2 – c.f x i
f
= 40 + 50-43 x 10
13
= 40 + 5.385 = 45.385
Class:
20-24
25-29 30-34
35-39 40-44
45-49
50-54
55-59
Frequency
3
5
20
6
3
1
10
Class
Frequency (f)
19.5-24.5
3
24.5-29.5
5
29.5-34.5
10 f0
34.5-39.5
20 f1
39.5-44.5
12 f2
44.5-49.5
6
49.5-54.5
3
54.5-59.5
1
12
Since we are given inclusive class
intervals,we first convert it into
exclusive one.
By inspection, modal class is 34.539.5
Z = l + f 1 – f0
xi=
2f1 – f0 – f2
= 34.5 + 10
x5
40-22
= 34.5 + 50
18
= 34.5 + 2.77
Z = 37.27
X
1990
1991
1992
1993
1994
Y
100
107
---
157
212
X
Y
1990
100
y0
1991
107
y1
1992
---
y2
1993
157
y3
1994
212
y4
Applying binomial Expansion,
Since the known values of Y are four, the
fourth leading differencewill be zeo. Thus,
= y4 – 4y3 + 6y2 -4y1 + y0
Subsituting the values of y’s, we get:
= 212 – 4(157) + 6y2 – 4y1 + y0 = 0
6y2 = 628 – 212 + 428 – 100
6y2 = 744
y2 = 124
Ques. Find out the rank
correlation.
X
10
15
15
20
18
16
15
Y
16
18
06
20
20
18
12
X
R1
Y
R2
D = R1-R2
D2
10
7
16
5.5
+1.5
2.25
15
5
18
3.5
+1.5
2.25
15
5
16
5.5
-0.5
0.25
20
1
20
1.5
-0.5
0.25
18
2
20
1.5
+0.5
0.25
16
3
18
3.5
-0.5
0.25
15
5
12
7
-2.0
4.00
∑D = 0
∑D2 = 9.5
N=7
R = 1 – 6 [ ∑D2 + 1/12(N3 – N)2 + … ]
N3 – N
= 1 – 6 [9.5 + 1/12(33 – 3) + 3/12(23 – 2) ]
73 – 7
= 1 – 6 [9.5 + 2 + 0.5 + 0.5 + 0.5]
336
= 1 – 6(13) = 1- 78 = 1 – 0.232 = 0.768
336
336
Given the following data:
N = 8, ∑X = 21 , ∑X2 = 99, ∑Y = 4, ∑Y2 = 68, ∑XY = 36
Find Out: (i) Regression equation X on Y and Y on X
(ii) Value of Y when X = 10 and
Value of X when Y = 2.5
Xm = ∑X = 21 , Ym = ∑ Y = 4
N 8
N 8
= 2.625
= 0.5
bxy = N. ∑XY – ∑X. ∑Y = 8 x 36 – (21)(4) = 288 – 84
N. ∑Y2 – (∑Y)2
8 x 68 – (4)2
544 – 16
= 204 = 0.38
528
(i) Regression Equation of X on Y
X – Xm = bxy (Y – Ym)
X – 2.625 = 0.38 (Y – 0.5)
X – 2.625 = 0.38Y – 0.19
X = 0.38Y + 2.435
Regression Equation of Y on X
Y – Ym = byx (X – Xm)
Y – 0.5 = 0.58 (X – 2.625)
Y – 0.5 = 0.58X – 1.5225
Y = 0.58X – 1.02
byx = N. ∑XY – ∑X. ∑Y = 8 x 36 – (21)(4) = 288 – 84
N. ∑X2 – (∑X)2
8 x 99 – (21)2
792 – 441
= 204 = 0.58
(ii) For X = 10, Y10 = 0.58(20) – 1.02 + 10.58
351
For Y = 2.5, X2.5 = 0.38(25) + 2.435 = 3.385
Statistics is a mathematical science pertaining to the
collection, analysis, interpretation or explanation, and
presentation of data. It also provides tools for prediction
and forecasting based on data. It is applicable to a wide
variety of academic disciplines, from the natural and social
sciences to the humanities, government and business.
Statistical methods can be used to summarize or describe a
collection of data; this is called descriptive statistics. In
addition, patterns in the data may be modeled in a way that
accounts for randomness and uncertainty in the
observations, and are then used to draw inferences about the
process or population being studied; this is called inferential
statistics. Descriptive, predictive, and inferential statistics
comprise applied statistics.

There is also a discipline called mathematical statistics, which
is concerned with the theoretical basis of the subject.
Moreover, there is a branch of statistics called exact statistics
that is based on exact probability statements.
The word statistics can either be singular or plural. In its
singular form, statistics refers to the mathematical science
discussed in this article. In its plural form, statistics is the
plural of the word statistic, which refers to a quantity (such as a
mean) calculated from a set of data.

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FUNCTIONS OF STATISTICS
Statistics is used for various purposes. It’s used to simplify
mass data and tomake comparisons easier. It’s also used to
bring out trends and tendenciesin the data as well as the
hidden relations between variables. All this helps tomake
decision making much easier. Let us look at each function of
statisticsin detail.
1)
Statistics simplifies mass data the use of statisticalconcepts helps in simplification of complex
data. Using statisticalconcept, the manager can make
decisions more easily. Thestatistical methods help in reducing
the complexity of the data andconsequently in the
understanding of any huge mass of data.



)
Statistics makes comparison easier Without using statisticalmethods and concepts, collection of
data and comparison can’t bedone easily. Statistics helps us to
compare data collected fromdifferent sources. Grand totals,
measures of central tendency,measures of dispersion, graphs
and diagrams, coefficient of correlation all provide ample
scopes for comparison.

Limitation of Statistics
Now a day’s statistics has become an inevitable part of our life.
Though the use and application of statistics isvast, it is not so
easy to collect information or data.Rather from the beginning of
the collection of data itsanalysis processing and explanation
etc. Steps haveample the probability of mistake in its
properapplication can be happened. Besides these,
statisticshas some limitation, some of which are
discussedbelow:
•
Statistics can analyze only aggregated observation or data

:
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Statistics given only overall measures:


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
statics gives us only anaverage or overall estimation. It is
almostimpossible to achieve a particular result. After
aprolonged observation as it is found in otherbranches of
knowledge. As the data are influencedby different factors, the
some result is notavailable every time.
•
Statistics rules are mutable
:
In some brunches of science some unchangeableprinciples
and data are available .but in statisticsthey are not found. The
principles of statistics arevariable and changeable,
approximate etc