Class 1TH YEAR Federal Board
2009
Paper:Statistics (Objective Type) Time
Allowed: Max.Marks:
Note:Use this paper to write the answers to the
objective questions.No marks will be awarded for cutting,over-writing
or using a pencil.This paper must be tagged with the answer-book.
1- Insert the correct option.
17
(i) What is the portion of the
table containing the column captions called ?
(a) Title
(b) Boxhead
(c) Stub
(d) Body of the table
(ii) What are the errors which tend to
occur in the same direction called ?
(a) Significant
digits
(b) Biased errors
(c) Random errors
(d) Chance errors
(iii) Hourly temperature recorded by weather
bureau is an example of.
(a) Continuous
& qualitative data
(b) Continous data
(c) Discrete
data
(d) Qualitativcontainse data
(iv) The data obtained from existing source
is called.
(a) Discrete
(b) Primary
(c) Secondary
(d) Continuous
(v) Which of the following is the correct
rounding off the number 4.003094
considering
that it contains only three significant digits ?
(a) 4.00
(b) 4.31
(c) 4.003
(d) 4.309
(vi) What is the classification said to be
when data are arranged by their time of occurance ?
(a) Discrete
(b) Geographical
(c) Qualitative
(d) Chronological
(vii) A graph showing cumulative frequencies plotted
against the upper class boundaries is called
(a) Polygon
(b) Barchart
(c) Ogive
(d) Frequency curve
(viii) When X and Y are independent then Var (X-Y)
is equal to:
(a) Var (X)--Var(Y)
(b) Var(X)+Var(Y)
(c) Var(X) +
Var(-Y)
(d) S.D(X) -S.D(Y)
(ix) Where the link relatives are used ?
(a) In fixed
base method.
(b) In chain base method
(c) In family
budget method.
(d) In consumer price index number.
(x) What is the sequence which folows
random or irregular npatterns of variation called ?
(a) Signal
(b) Noise
(c) Secular
(d) Seasonal
(xi) If r = 0.6,bxy=1.2;What is the volume
of byx ?
(a) 0.6
(b) 1.2
(c) 1.8
(d) 0.3
(xii) The best fitting trend is one for which sum
of squares of residuals is:
(a) Zero
(b) Least
(c) Negative
(d) Most
(xiii) For what value of Pab x pbc is the circular
test for price index Number satisfied ?
(a) V ab
(b) P ac
(c) P cb
(d) 1
(xiv) If we plot the paired observations (xi,
yi) on a graph;what is the resulting set of points called ?
(a) Ogive
(b) Polygon
(c) Histogram
(d) Scatter diagram
(xvi) The first moment X= 0 of a distribution is
12.08.the mean is:
(a) 10.80
(b) 10.08
(c) 12.08
(d) 12.88
(xvii) For a symmetrical distribution:
(a) B1
> n
(b) B1 = 0
(c) B1
< 0
(d) B1 = 3
2. Attempt any FOURTEEN
parts
(14 x 3 = 42)
(i) Differentiate between
diagrams and graphs.Write names of graphs of frequency distributions.
(ii) What are significant digits
? How many significant digits are there in each of the folowing
number ?
(a) 149.8
(b) 0.00273
(c) 1.048905
(d) 80.00
(e) 0.95
(f) 0.09001
(iii) A frequency table has four class
intervals with 5,9,18, 30 as frequencies in order. The left end
point
of third
class interval and mid point of fourth class interval are 20 and
35 respectivly.Set up the
frequency
table and calculate arithmetic mean.
(iv) The median, upper and lower quartiles
fourth and seventh deciles and fifteenth and 65th precentiles
of
a distribution of continous varible were calculate as 63.94, 66,50,
73.67, 72.0,60.93, 70.,75,
and
58.12. Identify the median, quartiles, deciles and percentiles.
(v) The A.M of the series is 30.5
marks, Find the missing value.
Marks
10 20
X 40
50
Frequency
08 10
20 15
07
(vi) Define absolute and relative measures
of dispersion. Write the qualities of a good measure.
(vii) Calculate the mean and variance dispersion
from the following data n = 150,
E(x-100) = 180,
E(x-100)2=245320
(viii) In a certain distribution the first
and second moments about the value 02 are -1 and 16
respectively.
Find the mean and variance of the distribution also calculate coefficient
of variation.
(ix) What would be the shape of the frequency
distribution if:
(a) Mean
= Median = Mode
(b) Mean > Median > Mode
(c) Mean
< Median < Mode
(d) Q3 - Median > Median - Q
Find coefficient
of range when Xm = 100 and Xo = 25.
(x) Distinguish between positive
and negative skewness with diagrams.
(xi) What is consumer price index ? How
is it constructed ? Write the formula of each method.
(xii) Distinguish between:
(a) Simple
linear and simple non linear regression.
(b) Perfect
positive and perfect negative correalte.
(xiii) Determine the estimated regression equation
y = a + bx if
(a) n
= 10, Ex =
20, Ey = 260,
Ex2 = 3144
(b) Ex
= 0
Ey = 245, Ex2 = 28,
n = 7
(xiv) What inference would you draw if correlation
coefficient is:
(a) +1
(b) -1
(c) 0
(d) -0.98
(e) 0.2
(f) 2
(xvi) Find the correlation coefficient from
the regression coefficients.
(a) 1.2
and 0.6
(b) -0.76 and -0.82
(c) - 1.6 and - 0.4
(xvii) Differentiate between single and noise. Write
the additive modle of the time series.
(xviii) Describe the merits and demerits of free hand semi
average and moving average method.lllustrate
each
method by one example.
(xix) (a) The semi average for 1964 - 1972
(both inclusive) are 82.5 and 104.Find the trend values b .
15
observations from 1986 to 2000 on real net sales is y = 2.4 + 0.5X
(1986 as base year).What
is the fitted trend value for this time series on real net sales
for the 5th year.
Attempt
any TWO question.
(2 x 13 = 26)
(3) Calculate the first four moments
about the value 7.95 and then the moments about the mean. Also
calculate
b2 is the distribution normal ?
Group
Frequency
Group
Frequency
3.5 - 4.4
05
8.5 - 9.4
11
4.5 - 5.4
10
9.5 - 10.4
10
5.5 - 6.4
13
10.5 - 11.4
04
6.5 - 7.4
17
11.5 - 12.4
01
7.5 - 8.4
29
(4) Calculate base year weighted and
current year weightd index number from the following data.
Also calculate
Fisher's index Number:
Items |
Base year |
Current year |
| |
Price |
Quantity |
Price |
Quantity |
A |
03 |
70 |
04 |
75 |
B |
05 |
80 |
06 |
90 |
C
|
08 |
40 |
10 |
55 |
D
|
10 |
50 |
12 |
60 |
(5) The marks obtained by 10 students in December
test (X) and promotion test (Y) are given below:
(i) Estimate the marks in the promotion
test (Y) if a student who was sick obtained 60 marks in the
December test
(X)
(ii) If a student who migrated after
the December test obtained 75 marks in the promotion test (Y),
estimate his
marks in the December test (X) had he been admitted earlier,
Students
X
Y
01
41
60
02
45
63
03
50
60
04
68
48
05
47
85
06
77
56
07
90
53
08
100
97
09
80
74
10
100
98 |
