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Ramjas College
University of Delhi, Delhi-110007
Aim of the PresentationThe main aim of this presentation is to show the students, the use of statistics in analyzing, presentation and making inferences from data in our day to day life.
The raw data for this project includes the “Marks of 250 students of a class”.
AcknowledgementsWe would like to extend our heartiest regard to our mentor and teacher Dr. Narinder Pushkarna or NP Sir who has guided us during the length and breadth of this highly demanding work and always supporting us in every way he could.
We would also like to thank our friends of Department of Statistics, Ramjas College who helped us in finishing this extensive deal.
Aayush, Poorva, Shubham, Sahiba
Raw Data32 48 41 41 39 47 53 51 30 1854 42 31 15 32 32 48 46 37 5638 62 50 38 35 26 51 40 42 2244 37 45 37 44 21 47 31 41 1868 38 30 52 42 41 34 52 60 3841 41 48 28 42 53 29 21 49 3630 32 37 29 38 33 49 35 37 4043 17 24 38 41 32 46 38 22 5046 38 26 23 25 50 46 15 42 5241 28 40 40 45 38 31 37 48 3040 35 42 51 56 33 38 36 42 4431 45 45 50 50 51 48 41 53 3240 49 40 34 38 43 28 34 44 5840 37 19 34 37 45 36 24 47 3336 38 61 44 50 32 45 30 43 3146 31 32 44 35 40 48 34 55 3948 53 43 43 41 50 34 55 39 4832 43 42 34 33 31 39 34 32 2440 47 27 34 34 50 42 47 44 3317 36 57 38 33 42 23 35 17 4648 31 31 33 26 50 37 58 44 2947 47 57 41 42 55 43 37 54 4537 42 47 44 44 52 19 46 50 3852 48 23 47 42 45 39 41 33 2448 40 60 38 38 44 48 38 44 43
Frequency DistributionInclusive type classification Exclusive type classification
Marks Number of students Marks Number of students
15-19 9 14.5-19.5 9
20-24 11 19.5-24.5 11
25-29 10 24.5-29.5 10
30-34 44 29.5-34.5 44
35-39 45 34.5-39.5 45
40-44 54 39.5-44.5 54
45-49 37 44.5-49.5 37
50-54 26 49.5-54.5 26
55-59 8 54.5-59.5 8
60-64 5 59.5-64.5 5
65-69 1 64.5-69.5 1
Associated Graphic Representations
17 22 27 32 37 42 47 52 57 62 670
10
20
30
40
50
60
911 10
44 45
54
37
26
85
1
Bar Graph showing the marks of students
NO OF STUDENTS
Class Marks
Num
ber
of
Stu
dents
Associated Graphic Representations
17 22 27 32 37 42 47 52 57 62 670
10
20
30
40
50
60
911 10
44 45
54
37
26
85
1
Frequency Polygon showing marks of students
NO OF STUDENTS
Class marks ( (u+l)/2 )
Num
ber
of
Stu
dents
Associated Graphic Representations
123456789101112
Pie Chart showing the marks of students
Arithmetic MeanAM is sum of all observations divided by total number of observations.
A.M. = Σfixi / Σfi
= 9930/250
CLASS MARKS NO OF STUDENTS
fixi
17 9 153
22 11 242
27 10 270
32 44 1408
37 45 1665
42 54 2268
47 37 1739
52 26 1352
57 8 456
62 5 310
67 1 67
Σ=250 Σ=9930
Harmonic MeanHM is sum of all observations divided by total number of observations.
H.M. =1/[ (1/N)* Σfi / xi]
=36.93
CalculationsMARKS CLASS MARKS NO OF STUDENTS CUMULATIVE
FREQUENCYfixi fixi
2
14.5-19.5 17 9 9 153 2601
19.5-24.5 22 11 20 242 5324
24.5-29.5 27 10 30 270 7290
29.5-34.5 32 44 74 1408 45056
34.5-39.5 37 45 119 1665 61605
39.5-44.5 42 54 173 2268 95256
44.5-49.5 47 37 210 1739 81733
49.5-54.5 52 26 236 1352 70304
54.5-59.5 57 8 244 456 25992
59.5-64.5 62 5 249 310 19220
64.5-69.5 67 1 250 67 4489
Total Σ=250 Σ=9930 Σ=418870
Median and Mode
Median class ---- 34.5 – 39.5Modal class ---- 39.5-44.5Median = l + (N/2-CF) * h/f
=34.5 + (135-74)*5/45 =34.5 + 6.77 = 41.27
Mode = l + [h*(f1 - f0 )/ (2f1 - f0 – f2 )]
=39.5 + [5*(54 - 45)/((2*54)-45-37)] =39.5 + 1.73 =41.23
Variance and Standard Deviation
Quantitative data vary about a measure of central tendency and these measures of deviations are called measures of dispersion or variation.
Variance=(1/N)*Σfixi2 -
[ (1/N)*Σfixi ] 2
= 92.93
Standard Variation = sqt(variance) = 9.64
MARKS CLASS MARKS NO OF STUDENTS fixi fixi2
14.5-19.5 17 9 153 2601
19.5-24.5 22 11 242 5324
24.5-29.5 27 10 270 7290
29.5-34.5 32 44 1408 45056
34.5-39.5 37 45 1665 61605
39.5-44.5 42 54 2268 95256
44.5-49.5 47 37 1739 81733
49.5-54.5 52 26 1352 70304
54.5-59.5 57 8 456 25992
59.5-64.5 62 5 310 19220
64.5-69.5 67 1 67 4489
Total Σ=250 Σ=9930 Σ=418870
Measure of Kurtosis and skewnessThe measures of the direction and degree of
asymmetry are called measures of skewness. The measures of the peakedness or flatness of
the frequency curves are called measures of kurtosis.
Skewness = -0.19553 ( as calculated from MS EXCEL )
