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Part I
(a) History about statitics
The Word statistics have been derived from Latin word Status or the Italian word
Statista, meaning of these words is Political State or a Government. Shakespeare used a
word Statist is his drama Hamlet (1602). In the past, the statistics was used by rulers. Theapplication of statistics was very limited but rulers and kings needed information about lands,
agriculture, commerce, population of their states to assess their military potential, their
wealth, taxation and other aspects of government.
Gottfried Achenwall used the word statistik at a German University in 1749 which
means that political science of different countries. In 1771 W. Hooper (Englishman) used the
word statistics in his translation of Elements of Universal Erudition written by Baron B.F
Bieford, in his book statistics has been defined as the science that teaches us what is the
political arrangement of all the modern states of the known world. There is a big gap between
the old statistics and the modern statistics, but old statistics also used as a part of the presentstatistics.
During the 18th century the English writer have used the word statistics in their works,
so statistics has developed gradually during last few centuries. A lot of work has been done in
the end of the nineteenth century.
At the beginning of the 20th century, William S Gosset was developed the methods for
decision making based on small set of data. During the 20th century several statistician are
active in developing new methods, theories and application of statistics. Now these days the
availability of electronics computers is certainly a major factor in the modern development ofstatistics.
(b) Application of statistics in everyday life.
(a) Scope of Statistics:
Statistics is not a mere device for collecting numerical data, but as a means of developing sound
techniques for their handling, analysing and drawing valid inferences from them. Statistics is applied in
every sphere of human activity social as well asphysical like Biology, Commerce, Education,
Planning, Business Management, Information Technology, etc. It is almost impossible to find a single
department of human activity where statistics cannot be applied. We now discuss briefly the
applications of statistics in other disciplines.
(b) Statistics and Industry:
Statistics is widely used in many industries. In industries, control charts are widely used to maintain a
certain quality level. In production engineering, to find whether the product is conforming to
specifications or not, statistical tools, namely inspection plans, control charts, etc., are of extreme
importance. In inspection plans we have to resort to some kind of sampling a very important aspect
of Statistics.
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(c) Statistics and Commerce:
Statistics are lifeblood of successful commerce. Any businessman cannot afford to either by under
stocking or having overstock of his goods. In the beginning he estimates the demand for his goods and
then takes steps to adjust with his output or purchases. Thus statistics is indispensable in business and
commerce. As so many multinational companies have invaded into our Indian economy, the size and
volume of business is increasing. On one side the stiff competition is increasing whereas on the otherside the tastes are changing and new fashions are emerging. In this connection, market survey plays an
important role to exhibit the present conditions and to forecast the likely changes in future.
(d) Statistics and Agriculture:
Analysis of variance (ANOVA) is one of the statistical tools developed by Professor R.A. Fisher, plays a
prominent role in agriculture experiments. In tests of significance based on small samples, it can be
shown that statistics is adequate to test the significant difference between two sample means. In
analysis of variance, we are concerned with the testing of equality of several population means. For an
example, five fertilizers are applied to five plots each of wheat and the yield of wheat on each of the
plots are given. In such a situation, we are interested in finding out whether the effect of these
fertilisers on the yield is significantly different or not. In other words, whether the samples are drawn
from the same normal population or not. The answer to this problem is provided by the technique of
ANOVA and it is used to test the homogeneity of several population means.
(e) Statistics and Economics:
Statistical methods are useful in measuring numerical changes in complex groups and interpreting
collective phenomenon. Nowadays the uses of statistics are abundantly made in any economic study.
Both in economic theory and practice, statistical methods play an important role. Alfred Marshall said,
Statistics are the straw only which I like every other economist have to make the bricks. It may alsobe noted that statistical data and techniques of statistical tools are immensely useful in solving many
economic problems such as wages, prices, production, distribution of income and wealth and so on.
Statistical tools like Index numbers, time series Analysis, Estimation theory, Testing Statistical
Hypothesis are extensively used in economics.
(f) Statistics and Education:
Statistics is widely used in education. Research has become a common feature in all branches of
activities. Statistics is necessary for the formulation of policies to start new course, consideration of
facilities available for new courses etc. There are many people engaged in research work to test thepast knowledge and evolve new knowledge. These are possible only through statistics.
(g) Statistics and Planning:
Statistics is indispensable in planning. In the modern world, which can be termed as the world of
planning, almost all the organisations in the government are seeking the help of planning for efficient
working, for the formulation of policy decisions and execution of the same. In order to achieve the
above goals, the statistical data relating to production, consumption, demand, supply, prices,
investments, income expenditure etc and various advanced statistical techniques for processing,
analysing and interpreting such complex data are of importance. In India statistics play an important
role in planning, commissioning both at the central and state government levels.
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(h) Statistics and Medicine:
In Medical sciences, statistical tools are widely used. In order to test the efficiency of a new drug or
medicine, t - test is used or to compare the efficiency of two drugs or two medicines, ttest for the two
samples is used. More and more applications of statistics are at present used in clinical investigation.
(i) Statistics and Modern applications:
Recent developments in the fields of computer technology and information technology have enabled
statistics to integrate their models and thus make statistics a part of decision making procedures of
many organisations. There are so many software packages available for solving design of experiments,
forecasting simulation problems etc.
SYSTAT, a software package offers mere scientific and technical graphing options than any other
desktop statistics package. SYSTAT supports all types of scientific and technical research in various
diversified fields as follows
1. Archeology : Evolution of skull dimensions
2. Epidemiology : Tuberculosis
3. Statistics : Theoretical distributions
4. Manufacturing: Quality improvement
5. Medical research: Clinical investigations.
6. Geology : Estimation of Uranium reserves from ground water
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Part II
The Ministry of Healthy has done many studies on the effort of food sold in the school canteen on children. To
support the government effort, you are required to run the project. This project required you to obtain the mass
and height of 100 students in certain forms of your school.
Based on the raw data collected, tabulate your data into a frequency table as below.
Answer:
Histogram 1
Mass of 100 students in kg
53 48 41 55 50 53 42 78 45 39
57 49 60 52 52 53 59 47 38 4252 47 54 44 62 45 39 60 44 52
58 47 96 50 44 56 41 44 56 42
53 36 64 45 48 77 44 44 54 49
60 48 57 49 47 52 70 50 43 60
53 56 58 48 55 64 42 53 58 44
53 45 62 50 45 41 62 70 50 43
75 67 68 50 52 60 68 38 65 96
98 64 50 50 54 54 54 48 65 73
Sais class interval = 12
Mass of students (kg) Tally Frequency
30 41 8
42 53 51
54 65 29
66 77 8
78 89 1
90 101 3
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45
40
35
29.5
30
25
20
15
10
65.553.541.5 101.589.577.5
5
0Lower boundary
(Mass of students)
50
Frequency
Mode = =49.3
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Histogram 2
Mass of 100 students in kg
53 48 41 55 50 53 42 78 45 39
57 49 60 52 52 53 59 47 38 42
52 47 54 44 62 45 39 60 44 52
58 47 96 50 44 56 41 44 56 42
53 36 64 45 48 77 44 44 54 49
60 48 57 49 47 52 70 50 43 60
53 56 58 48 55 64 42 53 58 44
53 45 62 50 45 41 62 70 50 43
75 67 68 50 52 60 68 38 65 96
98 64 50 50 54 54 54 48 65 73
Sais Class interval = 8
Mass of students (kg) Tally Frequency
36 43 14
44 51 32
52 59 29
60 67 14
68 75 6
76 83 2
84 91 092 99 3
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35
35.5
30
25
20
15
10
59.551.543.5 75.567.5
5
0
Lower boundary
(Mass of students)
Frequency
83.5 91.5 99.5
Mode = = 50.3
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Histogram 3
Mass of 100 students in kg
53 48 41 55 50 53 42 78 45 39
57 49 60 52 52 53 59 47 38 42
52 47 54 44 62 45 39 60 44 52
58 47 96 50 44 56 41 44 56 42
53 36 64 45 48 77 44 44 54 49
60 48 57 49 47 52 70 50 43 60
53 56 58 48 55 64 42 53 58 44
53 45 62 50 45 41 62 70 50 43
75 67 68 50 52 60 68 38 65 96
98 64 50 50 54 54 54 48 65 73
Sais class interval = 6
Mass of students (kg) Tally Frequency
36 41 8
42 47 22
48 53 29
54 59 16
60 65 1366 71 5
72 77 3
78 83 1
84 89 0
90 95 0
96 101 3
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35.5
30
25
20
15
10
53.547.541.5 101.559.5
5
0Lower boundary
(Mass of students)
Frequency
65.5 71.5 77.5 83.5 89.5 95.5
Mode = = 49.9
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i) Explain briefly, what you observe as the class size decreases and increasing the number of theclasses.
If you increase the number of classes in a histogram the columns become narrower, class
intervals become rounder and central tendency becomes more obvious meaning the data
becomes more accurate and any underlying information becomes more detailed as you are
able to collect more data and the histogram becomes more informative.
ii) Find mode for every histogram that you have drawn and interpret it.mode
Histogram 1 49.3
Histogram 2 50.3
Histogram 3 49.9
53 48 41 55 50 53 42 78 45 39
57 49 60 52 52 53 59 47 38 42
52 47 54 44 62 45 39 60 44 52
58 47 96 50 44 56 41 44 56 42
53 36 64 45 48 77 44 44 54 49
60 48 57 49 47 52 70 50 43 60
53 56 58 48 55 64 42 53 58 4453 45 62 50 45 41 62 70 50 43
75 67 68 50 52 60 68 38 65 96
98 64 50 50 54 54 54 48 65 73
The mode from the raw data is 50 (50 is got the highest frequency in the data). Histogram 3
which use the size class interval of 6, give me the accurate value of mode.
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Part III
a) Using the data from Table 1, complete Table 2 below.Mass of students (kg) Tally Frequency
30 41 8
42 53 5154 65 29
66 77 8
78 89 1
90 101 3
Table 1
Mass of
students (kg)Upper boundary Frequency
Cumulative
Frequency
30 41 41.5 8 8
42 53 53.5 51 59
54 65 65.5 29 88
66 77 77.5 8 96
78 89 89.5 1 97
90 101 101.5 3 100
Table 2
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b) Hence, draw an ogive based on the data.
Median
First Quartile
Third Quartile
90
80
70
29.5
60
50
40
30
20
65.553.541.5 101.589.577.5
10
0Upper boundary
(Mass of students)
100
Cumulative Frequency
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c) From the ogive, find median, first quartile, third quartile and interquartile range.i) Median
From graph =
ii) First quartile From graph =
iii) Third quartile From graph =
iv) Interquartile range = third quartile first quartile
= 60.1 46.3
= 13.8
d) Without drawing ogive,find median, first quartile, third quartile and interquartile range.
i) Median
Mass of
students (kg)Upper boundary Frequency
Cumulative
Frequency
30 41 41.5 8 8
42 53 53.5 51 59
54 65 65.5 29 88
66 77 77.5 8 96
78 89 89.5 1 9790 101 101.5 3 100
()
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ii) First Quartile
Mass of
students (kg)Upper boundary Frequency
Cumulative
Frequency
30 41 41.5 8 8
42 53 53.5 51 59
54 65 65.5 29 8866 77 77.5 8 96
78 89 89.5 1 97
90 101 101.5 3 100
()iii) Third Quartile
Mass of
students (kg)Upper boundary Frequency
Cumulative
Frequency
30 41 41.5 8 8
42 53 53.5 51 59
54 65 65.5 29 88
66 77 77.5 8 96
78 89 89.5 1 97
90 101 101.5 3 100
()v) Interquartile range = third quartile first quartile
= 60.12 45.5
= 14.62
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e) Stage the range and interquartile range. What is the different between the range andinterquartile range?
Range = highest data smallest data
= 98 36
= 62
Interquartile range = 14.62
The range is the difference between the highest and lowest value. The interquartile range is the
difference between the lower quartile and upper quartile in a set of date.
f) Calculate the mean, variance and standard deviations. Explain briefly why mean, variance andstandard deviations are used in statistic to interpret data.
Mass of
students (kg)
Frequency, Midpoint 30 41 8 35.5 284 10082
42 53 51 47.5 2422.5 115068.75
54 65 29 59.5 1725.5 102667.25
66 77 8 71.5 572 40898
78 89 1 83.5 83.5 6972.25
90 101 3 95.5 286.5 27360.75
()
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The mean, variance and standard deviation is used to quickly analyze data. Standard deviation
and variance are measures of the variation of the values in a data set around the mean of that
data set. Loosely speaking, the standard deviation is a measure of the average distance of the
values in the data set from their mean. The mean of a data set gives information about the
"balance point" of the distribution. The standard deviation adds information about how the
values in that data set are spread around the mean. So the standard deviation has a useful
interpretation on its own as a measure of spread/variability around the mean in any data set.
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Further Exploration
i)
TINGGI BERAT BMI BMI CATEGORIES
160 38 14.84 UNDERWEIGHT
165 42 15.43 UNDERWEIGHT
156 38 15.61 UNDERWEIGHT
158 39 15.62 UNDERWEIGHT
158 39 15.62 UNDERWEIGHT
178 50 15.78 UNDERWEIGHT
161 41 15.82 UNDERWEIGHT
161 41 15.82 UNDERWEIGHT
150 36 16.00 UNDERWEIGHT
172 48 16.22 UNDERWEIGHT
164 45 16.73 UNDERWEIGHT
184 57 16.84 UNDERWEIGHT157 42 17.04 UNDERWEIGHT
160 44 17.19 UNDERWEIGHT
160 44 17.19 UNDERWEIGHT
153 41 17.51 UNDERWEIGHT
163 47 17.69 UNDERWEIGHT
176 55 17.76 UNDERWEIGHT
164 48 17.85 UNDERWEIGHT
172 53 17.92 UNDERWEIGHT
153 42 17.94 UNDERWEIGHT
170 52 17.99 UNDERWEIGHT
170 52 17.99 UNDERWEIGHT
166 50 18.14 UNDERWEIGHT
166 50 18.14 UNDERWEIGHT
164 49 18.22 UNDERWEIGHT
175 56 18.29 UNDERWEIGHT
175 56 18.29 UNDERWEIGHT
178 58 18.31 UNDERWEIGHT
168 52 18.42 UNDERWEIGHT
156 45 18.49 UNDERWEIGHT183 62 18.51 NORMAL
154 44 18.55 NORMAL
169 53 18.56 NORMAL
155 45 18.73 NORMAL
160 48 18.75 NORMAL
151 43 18.86 NORMAL
181 62 18.92 NORMAL
178 60 18.94 NORMAL
178 60 18.94 NORMAL
150 43 19.11 NORMAL
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160 49 19.14 NORMAL
153 45 19.22 NORMAL
158 48 19.23 NORMAL
166 53 19.23 NORMAL
161 50 19.29 NORMAL
156 47 19.31 NORMAL
156 47 19.31 NORMAL
150 44 19.56 NORMAL
150 44 19.56 NORMAL
150 44 19.56 NORMAL
164 53 19.71 NORMAL
156 48 19.72 NORMAL
162 52 19.81 NORMAL
165 54 19.83 NORMAL
168 56 19.84 NORMAL
157 49 19.88 NORMAL
150 45 20.00 NORMAL
161 52 20.06 NORMAL
168 57 20.20 NORMAL
160 52 20.31 NORMAL
161 53 20.45 NORMAL
156 50 20.55 NORMAL
162 54 20.58 NORMAL
162 54 20.58 NORMAL
160 53 20.70 NORMAL
181 68 20.76 NORMAL167 58 20.80 NORMAL
161 54 20.83 NORMAL
145 44 20.93 NORMAL
162 55 20.96 NORMAL
169 60 21.01 NORMAL
160 54 21.09 NORMAL
141 42 21.13 NORMAL
158 53 21.23 NORMAL
153 50 21.36 NORMAL
153 50 21.36 NORMAL
148 47 21.46 NORMAL
152 50 21.64 NORMAL
166 60 21.77 NORMAL
171 64 21.89 NORMAL
171 64 21.89 NORMAL
170 64 22.15 NORMAL
164 60 22.31 NORMAL
172 67 22.65 NORMAL
160 58 22.66 NORMAL160 59 23.05 NORMAL
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180 75 23.15 NORMAL
176 73 23.57 NORMAL
178 77 24.30 NORMAL
156 62 25.48 OVERWEIGHT
164 70 26.03 OVERWEIGHT
153 65 27.77 OVERWEIGHT
166 78 28.31 OVERWEIGHT
157 70 28.40 OVERWEIGHT
152 68 29.43 OVERWEIGHT
148 65 29.67 OVERWEIGHT
178 96 30.30 OBESE
174 98 32.37 OBESE
168 96 34.01 OBESE
ii)
BMI CATEGORIES
NUMBER OF
STUDENTS PERCENTAGE
UNDERWEIGHT 31 31%
NORMAL 59 59%
OVERWEIGHT 7 7%
OBESE 3 3%
0%
10%
20%
30%
40%
50%
60%
UNDERWEIGHT NORMAL OVERWEIGHT OBESE
PERCENTAGE OF BMI IN THE SCHOOL
PERCENTAGE
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REFLECTION
In doing this project, there are some values that I have practiced as cooperation in group. I have
worked together with my friends from my school and also several friends from other school.
Other than that, I have learned about the meaning of patience during worked up for this assignment.
I also have learned how to persevere in doing the job.
Moreover, I was also adopted in cooperation it other partners to complete this work. Without help
from them, I will not be able to complete this task.
I would be a hard working and trying to finish this job properly and just in time.
Next, I also learned to be a person who does not easily give up in doing any work.
Student this section please do yourself ok......
Exercise regularly. While most people lead quite busy lives, the benefits of exercise usually present
themselves in all areas of your life. A simple way to start is walking. Studies have shown that walking 2
every day cuts the risk of death almost in half! Thirty minutes a day also works because it reduces as
much risk of a heart attack as a highly intense exercise.
Educate yourself. One of the most consistent markers of longevity across the world, in all economic
conditions, is higher education. If you stay in school and get a degree, it seems to increase your chances
of living longer more than almost anything else, apart from taking physical care of yourself with regular
exercise, eating healthy and not smoking.
Write a gratitude list. When you write a gratitude list, you will feel much better about yourself and you
won't think about what you don't have. When you focus on what you have now, you attract more good
things into your life. You will live longer because gratitude makes you feel happy.
Develop a sleep schedule. It is not as important to get a certain number of hours of sleep, so much as it
is to get the same amount of sleep, at the same time, day in and day out. Sleep gives your body a chance
to heal and regenerate; having a stable sleeping routine will help your body take care of itself more easily.
If you do not carry out successful sleep cycles over an extended period of time (48+ hours) you can
seriously affect your physical and mental health.