Upload
others
View
8
Download
0
Embed Size (px)
Citation preview
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
Page 5 of 27
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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.
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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)
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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: -
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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.
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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)
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
Page 15 of 27
(b)
(i)
(ii)
(iii)
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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)
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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)
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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: -
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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.
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
Page 25 of 27
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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
PRACTICALS FOR ICS STUDENTS FROM MODEL STATISTICS PRACTICAL NOTE BOOK
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)