Federal Board HSSC-I 2014
STATISTICS HSSC-I
SECTION — A
(Marks 17)
Time allowed: 25 Minutes
Marks: 17
NOTE: Section-A is compulsory. MI parts of this section are to be answered on the question paper itself. It should be completed in the first 25 minutes and handed over to the Centre Superintendent. Deleting/overwriting is not allowed. Do not use lead pencil.

Q.1
Circle the correct option i.e. A/B/C/D. Each part carries one mark.

• The data which have already been collected by someone are called

(A) Secondary data
(B) Primary data
(C) Arrayed data
(D) None of these

• A graph of cumulative frequency distribution is called

(A) Historigram
(B) Frequency polygon
(C) Ogive
(D) None of these

• Total angle of Pie chart is

( A) 270
(B) 300"
(C) 320'
(D) 360

• If a curve has a longer tail to the left, it is called a

(A) Symmetrical cure
(B) positively skewed curve
(C) Negatively skewed curve
(D) None of these

• If the mean is less than mode, the distribution is

(A) Positively skewed
(B) Negatively skewed
(C) Symmetrical
(D) None of these

• The most central value of an arrayed data is

(A) Mode
(B) Median
(C) Mean
(D) Harmonic mean

• The mode of 2, 10 and 7 is

(A) 10
(B) 2
(C) 7
(D) None of these

• In a symmetrical distribution, the mean, median and mode are

(A) Always equal
(B) Sometimes equal
(C) Never equal
(D) None of these

• For a certain distribution if (x -14) = 5, (x - 25) = 0 and  (x - 20) = 18 the value of mean is

(A) Zero
(B) 25
(C) 18
(D) 14

• The variance of a constant is equal to

(A) Constant
(B) Zero
(C) Unity
(D) None of these

• If x and y are independent, var (x-y) is equal to

(A) var(x) + var(y)
(B) var(x) - var(y)
(C) var(x+y)
(D) Zero

• If the third moment about mean is zero m3 = 0 the distribution is

(A) Mesokurtic
(B) Leptokurtic
(C) Symmetrical
(D) Platykurtic

• Second moment about mean is always equal to

(A) 0
(B) 1
(C) Variance
(D) Standard deviation

• The index given by ΣPnQn/ΣPoQo x 100 is

(A) The Laspeyre's index
(B) The Paasche's index
(C) The Value index
(D) None of these

• If Laspeyre's index number is 200, Paasche's index number is 200 the Fisher's index number is

(A) 100
(B) 200
(C) Zero
(D) 400

• Increased demand for coolers in summer and heaters in winter is an example of

(A) Secular trend
(B) Cyclical variation
(C) Seasonal variation
(D) Irregular variation

• In chain base method, the base period is

(A) Fixed
(B) Changed
(C) Constant
(D) None of these

SECTION - B
(Marks 42)

Q.2
Attempt any FOURTEEN parts. All parts carry equal marks.(14 x 3 = 42)

• Give three examples of Quantitative variable.
• Given the frequencies of 5 classes 2, 6,7,3,4. Find Cumulative frequencies and Relative frequencies.
• The mean of 10 numbers is 8. If an eleventh number is included, the mean becomes 9.What is the value of the eleventh number?
• The sum of deviations of 15 values from 20 is 45. Find Arithmetic Mean.
• Write three properties of Arithmetic Mean.
• Three teachers of statistics reported mean examination grades of 75, 82 and 85 for their classes which consisted of 30, 25 and 17 students. Determine the mean grade for all the classes.
• Define Quartile, Decile and Percentile.
• By adding 5 to each of numbers in the set 3, 6,2,1,5, we obtain 8,11,7,6,10. Show that the two sets have the same variance.
• Calculate Standard Deviation if n = 10,  u = 100,  u2 = 2212 and h=2.
• List any three methods for calculation dispersion.
• Compute base year weighted and current year weighted price index numbers for the
  given data:
  P0 g0 = 35310,          , Pnqn= 46707,
  Pn q0 = 41140   and  P0 qn = 39644
• Distinguish between an weighted index number and a weighted index number.
• Given n = 100,  x = 5000,  y = 6000, xy = 300300,  x2 = 25400 and E y2 = 360900.Calculate two regression co- efficient y on x and x on y.
• Describe the two lines of Regressions.
• Two regression lines are:
  Y       =       19.55 + 0.5423x
  X       =       3.62 + 1.2387y
  Find the correlation coefficient ' r’
• Given n = 10,  Dx = -8, Dy = 0,       Dx2 = 66,       Dy2 = 99 and  DxDy = 72 Calculate the correlation coefficient.
• State three properties of the correlation coefficient.
• Define Seasonal movements.
• What are the main components of time series?

SECTION - C
(Marks 26)

 Note: Attempt any TWO questions. All questions carry equal marks.(2 x 13 = 26)
Q.3
 (a) Find arithmetic mean, geometric mean and harmonic mean for the following data and Prove that AM > GM > HM:

  
(b) The first four moments of a distribution about x = 2.0 are 1, 2.5, 5.5 and 16.
Calculate:

• The first four moments about mean.
• Co-efficient of variation.

Q.4
Calculate base year weighted and current year weighted price index numbers. Also
         Calculate Fisher ideal price index number for the data given below:
Show that:
Fisher's Ideal index number =

Q.5                       
(a).Find correlation co-efficient rxy. Also find two regression co-efficients bxy and byx and
Prove that rxy =, for the following values of x and y:

                                               
(b) Compute 3 year and 5 year moving averages from the following data: