Healthy Diet (Student Copy)

7/31/2019 Healthy Diet (Student Copy)

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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


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


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


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


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


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


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


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











184 57 16.84 UNDERWEIGHT157 42 17.04 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







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.

Healthy Diet (Student Copy)

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