PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS ... · PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK Page 1 of 27 SECTION I Practical No 1: - The following

PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK

Page 1 of 27

SECTION I

Practical No 1: - The following data shows the number of heads in an experiment of tossing

5 coins 100 times. From a frequency distribution and construct a frequency polygon.

1, 5, 1, 2, 3, 2, 3, 1, 5, 3, 2, 0, 3, 1, 2, 1, 1, 0, 2, 1, 3, 1, 2, 4, 2, 3, 2, 0, 4, 2, 4, 2, 3, 1, 3, 4, 1,

0, 3, 2, 3, 2, 4, 3, 2, 3, 1, 3, 4, 1, 2, 3, 4, 3, 2, 0, 2, 1, 3, 1, 1, 5, 3, 2, 1, 3, 1, 2, 2, 3, 2, 0, 1, 2,

1, 2, 3, 2, 1, 3, 2, 3, 1, 2, 4, 1, 2, 1, 4, 2, 2, 3, 2, 5, 4, 2, 3, 3, 4, 3.

Answer: -

Maximum value = 5 , Minimum value = 0 (So discrete series is batter)

No. of heads (X) Tally Frequency (F)

0 6

1 23

2 30

3 26

4 11

5 4

Total 100


Page 2 of 27

Practical No 2: - The grades in mathematics of 80 students are as under:

68, 84, 78, 82, 72, 90, 62, 88, 76, 93, 73, 79, 88, 73, 68, 93, 71, 59, 85, 75, 61, 65, 75, 87, 60,

92, 95, 78, 63, 72, 66, 78, 82, 75, 74, 77, 69, 74, 88, 60, 96, 78, 89, 61, 94, 95, 60, 69, 83, 71,

79, 62, 67, 97, 75, 85, 76, 65, 71, 75, 65, 80, 73, 57, 78, 62, 76, 78, 53, 74, 86, 67, 73, 81, 88,

63, 76, 75, 85, 77.

From a frequency distribution grouping in intervals of 5 grades as 50----54, 55----59, etc.

Draw a histogram for the distribution obtained.

Answer: -

Grades Tally Frequency C.B

50----54 1 49.5----54.5

55----59 2 54.5----59.5

60----64 10 59.5----64.5

65----69 10 64.5----69.5

70----74 12 69.5----74.5

75----79 20 74.5----79.5

80----84 6 79.5----84.5

85----89 10 84.5----89.5

90----94 5 89.5----94.5

95----99 4 94.5----99.5

Total


Page 3 of 27

Practical No 3: - The data given below shows the diameters in inches of ball-bearings

manufactured by a company:

73.1, 47.7, 84.2, 64.2, 64.5, 72.4, 84.6, 74.6, 48.1, 66.0, 78.3, 63.1, 84.1, 61.3, 84.0, 83.4,

77.2, 84.7, 78.1, 77.5, 56.6, 73.8, 80.1, 58.4, 71.2, 94.2, 93.7, 72.1, 64.2, 71.5, 78.5, 74.7,

86.4, 67.8, 56.3, 48.2, 82.1, 72.0, 94.3, 70.4, 84.9, 70.8, 66.9, 78.0, 74.4, 39.3, 54.1, 78.3,

51.0, 72.3

(a) Prepare a frequency distribution using the following grouping 35----39.9, 40----44.9,...

(b) Draw an Ogive for this distribution

Answer: -

Grades Tally Frequency C.B C.F

35----39.9 1 34.95----39.95 1

40----44.9 0 39.95----44.95 1

45----49.9 3 44.95----49.95 4

50----54.9 2 49.95----54.95 6

55----59.9 3 54.95----59.95 9

60----64.9 5 59.95----64.95 14

65----69.9 3 64.95----69.95 17

70----74.9 13 69.95----74.95 30

75----79.9 7 74.95----79.95 37

80----84.9 9 79.95----84.95 46

85----89.9 1 84.95----89.95 47

90----94.9 3 89.95----94.95 50

Total 50


Page 4 of 27

Practical No 4: - Height measurements of second year students of a certain college at

Lahore, recorded to the tenth of a cm are given below:

169.7, 176.2, 174.8, 165.6, 172.9, 171.9, 176.4, 173.8, 162.3, 178.9, 168.3, 180.2, 166.7,

179.5, 184.2, 161.8, 175.6, 171.5, 165.5, 176.3, 174.8, 176.5, 169.3, 171.5, 184.3, 181.2,

162.6, 176.0, 178.3, 182.8, 180.6, 178.9, 166.7, 179.3, 172.7, 181.2, 164.5, 171.9, 163.5,

164.7

(a) Make a frequency distribution taking a suitable class interval size.

(b) Draw a histogram for the frequency distribution obtained in (a) above.

Answer: -

Minimum value = 161.8 , Maximum value = 184.3

Range = 184.3 – 161.8 = 22.5 , No. of groups = 1 + 3.3 log(40) = 6.3 or 6

Class interval = 22.5/6 = 3.7 or 4

Class Limits Tally Frequency C.B

160.0----163.9 4 159.95----163.95

164.0----167.9 5 163.95----167.95

168.0----171.9 7 167.95----171.95

172.0----175.9 6 171.95----175.95

176.0----179.9 10 175.95----179.95

180.0----183.9 6 179.95----183.95

184.0----187.9 2 183.95----187.95

Total


Page 5 of 27


Page 6 of 27

Practical No 5: - Read the following passage:

“The exalted Quran is a store house of universal knowledge and Divine Mysteries and

Transpose. It has a style which moves the hearts and induces such fear of Allah Almighty

that the hair on the body stand on edge when it is recited. The soul becomes ecstatic and

intellect of man is stunned while listening to it; and windows of light of spiritual

consciousness and material knowledge are opened on its student. Admittedly the Grand

Quran is an eternal spring on which mankind can drink deep to attain enduring success in

this world as well as in the hereafter”.

Count the number of letters in each word. Make a frequency distribution of the word length

X. Compute the mean, G.M, S.D and C.V for this distribution.

Answer: -

Let number of letters = X

X Tally F FX log X F log X X2 FX

2

1 2 2 0 0 1 2

2 23 46 0.30103 6.92369 4 92

3 18 54 0.477121 8.588183 9 162

4 11 44 0.60206 6.62266 16 176

5 15 75 0.69897 10.48455 25 375

6 5 30 0.778151 3.890756 36 180

7 10 70 0.845098 8.45098 49 490

8 4 32 0.90309 3.61236 64 256

9 9 81 0.954243 8.588183 81 729

10 1 10 1 1 100 100

11 0 0 1.041393 0 121 0

12 0 0 1.079181 0 144 0

13 1 13 1.113943 1.113943 169 169

99 457 59.2753 2731


Page 7 of 27

Practical No 6: - Make a frequency distribution of the vowels (a, e, i, o, u) from the

following paragraph. Find the modal letter from this distribution. Draw bar chart to depict

the frequency of each vowel.

“The illustrious Quran embodies Allah’s last massage and the universal law for mankind. In

this changing world where mutations in time and space are constantly giving rise to ever new

questions and problems, perfect answers can be expected from the divine word of the

almighty creator only. Had it not been for an immutable and perpetual law governing

principle and permanent aspects of existence, mankind would never have taken the course of

unity and harmony. During the last 1400 years, people all over the globe have bowed to the

enduring truth of this final law of survival vouchsafed to man by almighty Allah”

Answer: -

Vowel Tally Frequency

a 46

e 60

i 32

o 31

u 16

Model letter is “e” as it occurs greatest number of times.


Page 8 of 27

Practical No 7: - Here is a passage from a book. If X denotes the number of vowels in each

word, make a frequency distribution for X. Find its mode and median.

“We often hear that this is the information age, and it is certainly true that the economy runs

on information. A firm needs information on the best way to produce its products, given

limited resources and the current technology; a consumer needs information to make

consumption decisions, given a limited budget; and a government needs information on its

society and the global community to best formulate a set of laws and regulations, subject to

its constitutional restrictions. If economic actors are to function efficiently, given the

restrictions under which they operate, there must be a steady flow of information.”

Answer: -

Number of vowels in each word = X

Maximum length of the word = 6

Minimum length of the word = 1

X Tally Frequency C.F

1 50 50

2 21 71

3 11 82

4 9 91

5 7 98

6 1 99

Mode = 1 (most repeated value)


Page 9 of 27

Practical No 8: - From a bivariate frequency distribution of the following data of ages of

husbands and wives at marriage into 6 and 5 classes respectively. Ages of husbands 16 20 20 25 18 26 26 30 28 30 26 27 28 29 25 25

Ages of wives 20 17 18 20 16 27 25 25 30 25 25 23 25 20 20 27

Ages of husbands 23 26 30 29 21 23 25 28 18 17 20 25 30 25 25 27

Ages of wives 18 23 21 30 19 25 18 25 20 16 22 16 27 23 25 24

Ages of husbands 28 29 29 27 26 25 24 26 27 28 21 22 23 24 27 31

Ages of wives 25 27 24 28 26 25 23 23 27 26 20 20 25 26 30 30

Ages of husbands 28 26 20 22 24 24 20 27 26 29 16 19 22 18 20 27

Ages of wives 29 26 20 22 24 20 23 30 28 30 16 20 19 20 25 23

Answer: -

Maximum age of husband = 31

Minimum age of husband = 16

Range for husband’s age = 31-16 = 15

Maximum age of wife = 30

Minimum age of wife = 16

Range for wife’s age = 30-16 = 14

According to the range of husband’s and wife’s 5 class limits are suitable.

Ages of wives Ages of husbands

16----18 19----21 22----24 25----27 28----30 31----33

16----18

19----21

22----24

25----27

28----30

Ages of wives Ages of husbands Total

16----18 19----21 22----24 25----27 28----30 31----33

16----18 3 2 1 2 8

19----21 3 4 3 2 2 14

22----24 9 2 3 6 1 12

25----27 9 1 3 9 8 21

28----30 9 9 4 4 1 9

Total 6 9 10 23 15 1 64


Page 10 of 27

Practical No 9: - Calculate mean, geometric mean, harmonic median and mode for the

following distribution of members of the house hold:

Member of the household (X) 1 2 3 4 5 6 7 8 9 10 11 12 13

Number of houses (F) 1 3 7 21 32 42 50 35 25 15 15 10 3

Answer: -

X F FX log X F log X F/X C.F

1 1 1 0 0 1 1 2 3 6 0.30103 0.90309 1.5 4

3 7 21 0.477121 3.339849 2.333333 11 4 21 84 0.60206 12.64326 5.25 32 5 32 160 0.69897 22.36704 6.4 64 6 42 252 0.778151 32.68235 7 106 7 50 350 0.845098 42.2549 7.142857 156 8 35 280 0.90309 31.60815 4.375 191 9 25 225 0.954243 23.85606 2.777778 216

10 15 150 1 15 1.5 231 11 15 165 1.041393 15.62089 1.363636 246 12 10 120 1.079181 10.79181 0.833333 256 13 3 39 1.113943 3.34183 0.230769 259 259 1853 214.4092 41.70671


Page 11 of 27

Practical No 10: - Compute mode, median, Q1, Q3, D6 and P74 for the following data:

Groups Class Boundaries F C.F

0.3736----0.3739 0.37355----0.37395 2 2

0.3740----0.3743 0.37395----0.37435 15 17

0.3744----0.3747 0.37435----0.37475 32 49

0.3748----0.3751 0.37475----0.37515 62 111

0.3752----0.3755 0.37515----0.37555 103 214

0.3756----0.3759 0.37555----0.37595 95 309

0.376----0.3763 0.37595----0.37635 28 337

0.3764----0.3767 0.37635----0.37675 12 349

0.3768----0.3771 0.37675----0.37715 8 357

0.3772----0.3775 0.37715----0.37755 3 360

360

Answer: -


Page 12 of 27

Practical No 11: - The following data gives the annual earnings (in thousand rupees) before

taxes for 36 families randomly selected from the e1995 interview survey conducted by the

Federal Bureau of Statistics:

11.5, 55.0, 27.7, 21.6, 10.9, 18.8, 9.0, 29.0, 23.3, 8.0, 12.4, 43.0, 5.0, 35.0, 34.8, 34.3, 40.0,

22.7, 26.0, 26.1, 20.0, 8.9, 16.6, 14.7, 47.4, 19.9, 6.9, 43.0, 16.2, 8.0, 14.0, 28.0, 48.6, 58.0,

25.0, 16.8

(a) Show that A.M ≥ G.M

(b) Make a frequency distribution taking the class interval size as 6 and lower limit as 5.0,

then show that A.M ≥ G.M

(c) Is there any difference in the results of (a) and (b)?

Answer: -

(a)

X X log X log X

11.5 26.1 1.0607 1.41664

55 20 1.74036 1.30103

27.7 8.9 1.44248 0.94939

21.6 16.6 1.33445 1.22011

10.9 14.7 1.03743 1.16732

18.8 47.4 1.27416 1.67578

9 19.9 0.95424 1.29885

29 6.9 1.4624 0.83885

23.3 43 1.36736 1.63347

8 16.2 0.90309 1.20952

12.4 8 1.09342 0.90309

43 14 1.63347 1.14613

5 28 0.69897 1.44716

35 48.6 1.54407 1.68664

34.8 58 1.54158 1.76343

34.3 25 1.53529 1.39794

40 16.8 1.60206 1.22531

22.7

1.35603

26.0

1.41497

886.1 47.2772

Hence proved A.M ≥ G.M


Page 13 of 27

(b)

Frequency distribution when class interval size = 6 and lower limit of first group = 5.0

Groups Tally F X FX Log X F log X

5.0----10.9 7 7.95 55.65 0.900367 6.30257

11.0----16.9 7 13.95 97.65 1.144574 8.012019

17.0----22.9 5 19.95 99.75 1.299943 6.499715

23.0----28.9 6 25.95 155.7 1.414137 8.484824

29.0----34.9 3 31.95 95.85 1.504471 4.513413

35.0----40.9 2 37.95 75.9 1.579212 3.158424

41.0----46.9 2 43.95 87.9 1.642959 3.285918

47.0----52.9 2 49.95 99.9 1.698535 3.397071

53.0----58.9 2 55.95 111.9 1.7478 3.4956

36 880.2 47.14955

Again proved A.M ≥ G.M

(c) There is a small difference between the results of parts (a) and (b). This difference is

due to the grouping error because all the values lying in a group are assumed to be identical

to X (class marks) but actually it is not so.


Page 14 of 27

Practical No 12: - The weight measurements in grams of 20 eggs are given as under:

65, 68, 60, 76, 65, 74, 58, 56, 61, 57, 63, 64, 72, 56, 65, 67, 65, 63, 67, 67.

(a) Mode, median, Q1, Q3, mean and standard deviation.

(b) Find the percentage of observations lying within (i) (ii) (iii)

Answer: -

S.N0. X X2 Arranged X

1 65 4225 56

2 68 4624 56

3 60 3600 57

4 76 5776 58

5 65 4225 60

6 74 5476 61

7 58 3364 63

8 56 3136 63

9 61 3721 64

10 57 3249 65

11 63 3969 65

12 64 4096 65

13 72 5184 65

14 56 3136 67

15 65 4225 67

16 67 4489 67

17 65 4225 68

18 63 3969 72

19 67 4489 74

20 67 4489 76

1289 83667

(a)

Mode = 65 (most repeated value)


Page 15 of 27

(b)

(i)

(ii)

(iii)


Page 16 of 27

Practical No 13: - Given the following distribution, calculate

(i) Mean deviation form mean

(ii) Quartile deviation

(iii) Coefficient of skewness by Bowley’s method Groups 10.0----10.4 10.5----10.9 11.0----11.4 11.5----11.9 12.0----12.4 12.5----12.9 13.0----13.4

Frequency 4 7 25 20 19 3 2

Answer: -

Groups F X FX C.B C.F

10.0----10.4 4 10.2 40.8 -1.375 1.375 5.5 9.95----10.45 4

10.5----10.9 7 10.7 74.9 -0.875 0.875 6.125 10.45----10.95 11

11.0----11.4 25 11.2 280 -0.375 0.375 9.375 10.95----11.45 36

11.5----11.9 20 11.7 234 0.125 0.125 2.5 11.45----11.95 56

12.0----12.4 19 12.2 231.8 0.625 0.625 11.875 11.95----12.45 75

12.5----12.9 3 12.7 38.1 1.125 1.125 3.375 12.45----12.95 78

13.0----13.4 2 13.2 26.4 1.625 1.625 3.25 12.95----13.45 80

80 926 42

(i)

(ii)

(iii)


Page 17 of 27

Practical No 14: - From the given distribution, calculate:

(i) Mean, median, mode, S.D and C.V

(ii) Find coefficient of skewness by Karl Pearson’s formula

Class Limits 3----3.9 4----4.9 5----5.9 6----6.9 7----7.9 8----8.9

Frequency 1 27 210 413 509 447

Class Limits 9----9.9 10----10.9 11----11.9 12----12.9 13----13.9

Frequency 234 99 23 6 1

Answer: -

Class Limits F X FX C.B C.F X2 FX

2

3----3.9 1 3.45 3.45 2.95----3.95 1 11.9025 11.9025

4----4.9 27 4.45 120.15 3.95----4.95 28 19.8025 534.6675

5----5.9 210 5.45 1144.5 4.95----5.95 238 29.7025 6237.525

6----6.9 413 6.45 2663.85 5.95----6.95 651 41.6025 17181.83

7----7.9 509 7.45 3792.05 6.95----7.95 1160 55.5025 28250.77

8----8.9 447 8.45 3777.15 7.95----8.95 1607 71.4025 31916.92

9----9.9 234 9.45 2211.3 8.95----9.95 1841 89.3025 20896.79

10----10.9 99 10.45 1034.55 9.95----10.95 1940 109.2025 10811.05

11----11.9 23 11.45 263.35 10.95----11.95 1963 131.1025 3015.358

12----12.9 6 12.45 74.7 11.95----12.95 1969 155.0025 930.015

13----13.9 1 13.45 13.45 12.95----13.95 1970 180.9025 180.9025

1970 15098.5 895.4275 119967.7

(i)

(ii)


Page 18 of 27

Practical No 15: - A distribution consists of 4 components with frequencies 108, 122, 150,

175 having means 29.2, 18.7, 16.8, 19.3 and standard deviations 2.9, 4.6, 3.7 and 4.2

respectively. Find the coefficient of variation for the combined distribution.

Answer: -


Page 19 of 27

Practical No 16: - Find first four moments about mean for the following distribution. Also

calculate moment ratios β1 and β2.

Group 10----14 15----19 20----24 25----29 30----34 35----39

Frequency 2 4 6 8 3 1

Answer: -

Group F X FX

10----14 2 12 24 -11.875 -23.75 282.03125 -3349.121094 39770.81299

15----19 4 17 68 -6.875 -27.5 189.0625 -1299.804688 8936.157227

20----24 6 22 132 -1.875 -11.25 21.09375 -39.55078125 74.15771484

25----29 8 27 216 3.125 25 78.125 244.140625 762.9394531

30----34 3 32 96 8.125 24.375 198.046875 1609.130859 13074.18823

35----39 1 37 37 13.125 13.125 172.265625 2260.986328 29675.44556

24 573 0 940.625 -574.21875 92293.70117


Page 20 of 27

Practical No 17: - The following sums have been obtained from a frequency distribution of

variable X after making the substitution X = 10 + 5U.

(a) Calculate mean, variance, b1 and b2.

(b) Would you consider the distribution to be normal?

Answer: -

(a)

First four moments about mean

(b)

As b2 < 3, the distribution is platykurtic.


Page 21 of 27

Practical No 18: - Average of whole sale prices of 4 commodities are given below:

Year Wheat Rice Sugar Mutton

1985 60.68 203.95 246.72 827.20

1986 68.75 228.64 278.80 858.70

1987 73.79 230.18 296.50 884.25

1988 77.50 233.36 309.42 940.48

1989 85.69 237.50 331.50 994.50

1990 88.75 271.92 354.75 1058.75

1991 85.84 313.50 388.20 1185.00

1992 88.75 331.42 404.25 1334.25

Find the chain indices using median as average.

Answer: -

Year

Link relatives

Median

Chain indices Wheat Rice Sugar Mutton

1985

= 100

=100

=100

=100

100 100

1986

= 113.30

=112.11

=113.00

=103.81

112.56

=112.56

1987

= 107.33

=100.67

=106.35

=102.98

104.67

=117.82

1988

= 103.03

=101.38

=104.36

=106.36

104.70

=109.59

1989

= 110.57

=101.77

=107.14

=105.74

106.44

=111.44

1990

= 103.57

=114.49

=107.01

=106.46

106.74

=113.61

1991

= 96.72

=115.29

=109.43

=111.92

110.68

=118.61

1992

= 103.39

=105.72

=104.13

=112.59

104.92

=116.13


Page 22 of 27

Practical No 19: - Prices of 5 commodities are given for the years 1980 to 1985. Construct

price index numbers by

(i) Simple aggregative method taking 1980 as base

(ii) Simple average of relatives taking 1980 as base

Commodity Prices

1980 1981 1982 1983 1984 1985

A 90 72 100 95 80 90

B 87 64 90 88 95 100

C 130 135 110 154 160 170

D 65 60 102 98 100 105

E 70 68 98 104 110 103

Answer: -

(i) Commodity Prices

1980 1981 1982 1983 1984 1985

A 90 72 100 95 80 90

B 87 64 90 88 95 100

C 130 135 110 154 160 170

D 65 60 102 98 100 105

E 70 68 98 104 110 103

Total 442 399 500 539 545 568

(ii) Year A B C D E Index Number.

(using mean)

1980

1981

1982

1983

1984

1985


Page 23 of 27

Practical No 20: - Construct chain indices for the following data of price relatives using

G.M as average.

Price relatives

Year Sugar Rice Tea Coffee

1960 100 98 85 100

1961 103 92 80 105

1962 120 102 77 110

1963 112 107 90 98

1964 115 112 95 102

Answer: -

Link relatives

Year Sugar Rice Tea Coffee G.M Chain indices

1960 100 98 85 100 95.53 95.53

1961

= 103

=93.88

=94.12

=105

98.87

= 94.45

1962

=116.50

=110.09

=96.25

=104.76

106.83

=100.90

1963

=93.33

=104.9

=116.9

=98

104.88

=105.83

1964

=102.68

=

=104.67

=104.08

99.87

=105.69


Page 24 of 27

Practical No 21: - Given the data below, construct the following price index numbers for the

year 1998 and 1999, taking 1990 as base.

(i) Laspeyre’s (ii) Paasche’s (iii) Fisher’s

Commodity Prices Quantities

1990 1998 1999 1990 1998 1999

A 12 15 18 105 120 130

B 9 10 13 90 95 112

C 6 8 10 52 60 62

D 5 7 8 35 37 45

E 7 9 12 48 56 60

Answer: -

Commodity Prices Quantities

1990(p0) 1998(p1) 1999(p2) 1990(q0) 1998(q1) 1999(q2)

A 12 15 18 105 120 130

B 9 10 13 90 95 112

C 6 8 10 52 60 62

D 5 7 8 35 37 45

E 7 9 12 48 56 60

Necessary calculation

Commodity p1q0 p0q0 p1q1 p0q1 p2q0 p2q2 p0q2

A 1575 1260 1800 1440 1890 2340 1560

B 900 810 950 855 1170 1456 1008

C 416 312 480 360 520 620 372

D 245 175 259 185 280 360 225

E 432 336 504 392 576 720 420

Total 3568 2893 3993 3232 4436 5496 3585


Page 25 of 27


Page 26 of 27

Practical No 22: - A family budget enquiry was conducted by the science college (statistics)

students for one of the household of a college block. The following data was obtained:

Item Quantity consumed

in 1975

Unit of price Price

1992 2002

Wheat 260 kg Per 40 kg 180 300

Rice 80 kg Per 40 kg 480 850

Sugar 100 kg Per one kg 12 20

Ghee 60 kg Per one kg 30 52

Milk 750 litre Per one litre 5 12

Vegetable 200 kg Per one kg 4 6

Fuel 160 kg Per 40 kg 110 200

Cloth 60 meter Per one meter 25 52

Calculate consumer’s price index number using (i) Aggregative expenditure method

(ii) Household budget method taking 1992 as base.

Answer: -

Item Quantity consumed

in 1975(q0)

Unit of price Price

1992(p0) 2002(p1)

Wheat

Per 40 kg 180 300

Rice

Per 40 kg 480 850

Sugar 100 kg Per one kg 12 20

Ghee 60 kg Per one kg 30 52

Milk 750 litre Per one litre 5 12

Vegetable 200 kg Per one kg 4 6

Fuel

Per 40 kg 110 200

Cloth 60 meter Per one meter 25 52


Page 27 of 27

Necessary calculations

Item p1q0 p0q0 = I

Wheat 1950 1170

195000

Rice 1700 960

170000

Sugar 2000 1200

200000

Ghee 3120 1800

312000

Milk 9000 3750

900000

Vegetable 1200 800

120000

Fuel 800 440

80000

Cloth 3120 1500

312000

Total 22890 11620 2289000

(i)

(ii)

Documents

PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS ... · PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK Page 1 of 27 SECTION I Practical No 1: - The following