1. SOCIAL NETWORK AS A VENUE OF PARTICIPATION AND SHARING AMONG TEENAGERS
SWITCH PROJECT
STAFF AND STUDENTS WORKING TOGETHER FOR CHANGE
SOCIAL NETWORK AS A VENUE OF PARTICIPATION AND SHARING AMONG TEENAGERS
MATHEMATICS FOR REAL LIFE
INTELLECTUAL OUTPUT 5
BY LIDIA BIANCO ITE TAMBOSI BATTISTI
Disclaimer: This publication reflects only the author’s views and the European Commission and UK NA are not responsible for any use that may be made of the information it contains.

2. STATISTICS INTRODUCTION

3. Statistics is defined as a set of scientific methods for the study of collective phenomena. The study of a phenomenon addresses the whole population or a subset of elements called sample.

4. Units of statistics and population

5. The set of units represents the collective or the population

6. Sample

7. Group of elementary units that form a subset of the population
Group of elementary units that form a subset of the population. The sample has to represent population to infer from the sample information about population. The sample allows to reduce costs and examine in depth some aspects...

8. Samples can be constructed in a way that’s:
direct – when the interview is conducted by an operator properly trained; the cost is a bit high but they present less mistakes of compilation.   
indirect – interviews conducted via phone or through the sending of a questionnaire by post or .

9. Some preliminary definitions

10. The variable: each element of a population, known as statistic units are named variable.

11. Statistic Variable: the collective phenomenon is presented in different ways in various statistic units, so we call it statistic variable.

12. The statistics variables are of type:
• qualitative
• quantitative

13. Qualitative: Its methods are not expressed by numbers and represent a changeable statistic, which are represented by adjectives. Example: study title, nationality etc.

14. Discrete if the values that it can undertake are integers Example:
Quantitative:
Discrete if the values that it can undertake are integers
Example:
- Number of products produced .
Continue if the values that it can undertake are non integers
- weight, length

15. Object of the statistic: study of a phenomenon, pulling valid conclusions and taking reasonable decisions

16. Through surveys with scientific methods of the statistic:
1.Describe
2. Generalize
3. Provide

17. The statistic is divided in: 1. descriptive 2. inferential

18. INFERENTIAL STATISTIC
Procedure in which through observed characteristics of a sample you try to infer the ones of the population of reference.

19. Inferential statistic:
Procedure in which through observed characteristics of a sample you try to infer the ones of the population of reference.

20. DESCRIPTIVE STATISTIC

21. Stages of the statistical survey for the study of a phenomenon

22. Statistical surveys are classified in: Census:
The only survey of this type is the census that is done every 10 years and detects the whole population.
samples:
Only one part of the population is interviewed and it’s called sample, which presumably, should represent well the population. Classifying instead, based on how the interview is conducted, we have surveys.

23. Planning of our surveys

24. 1^ phase of planning:
the theme for the chosen project of survey collectively decided, addresses two second year classes of Tambosi in Trento, with the purpose of finding out what they do with social media.

25. 2^ phase:
The gathering of data is done through a questionnaire with multiple choice questions, prepared with google forms from some students, and sent to classmates by .

26. The questionnaire

27. 3^ phase :
in this phase unrefined data is detected and organised in tables from the students that gather them in tables on electronic papers.

28. Elaboration

29. • they costruct diagrams, histograms,etc..
4^ phase elaboration:
• they calculate absolute frequencies and percentages, statistical indices, indices of linear correlation with excel.
• they costruct diagrams, histograms,etc..

30. Let’s start calculating the frequencies of the obtained answers

31. ABSOLUTE FREQUENCY : The frequency of a value is the number of individuals of the population for which the variable assumes the same value.

32. Relative frequency: Is the ratio between the value of the frequency and the number of individuals of the population. relat.freq.= abs.freq. / total individuals

33. Percentage frequency:
You obtain it by normalising to a 100 the total of the population.
percentage freq. = relative freq. * 1 00

34. Tabulation and representation of some of our unrefined data

38. Let’s start the mains statistical indices

39. Statistical indices of: • central tendency • dispersion

40. Indices of central tendency
Measures of central tendency are the tendency of quantitative data to cluster around some central value; the purpose of these indices is:

41. Purpose The purpose of the indices is to summarize a certain characteristic and to compare different situations. Some of the indices are: The mean The mode The median

42. Simple arithmetic mean
Simple arithmetic mean = sum of all the measurements I number of observations in the data set
N = number of individuals of a population
X = numerical variable
xi = value that the variable takes on upon each individual of the population
La mean is defined by Xm = Xl+X2+…xn/n

43. Mode
It’s called mode (or sample mode) of the elements, the element (or the elements) of which the maximum absolute frequency corresponds to.
It’s easy to deduct that the sample mode isn’t influenced by extreme values and can also be used for non-numerical data, so qualitative data. You can observe that the sample mode doesn’t exist or isn’t unique.

44. Median: the median of a collection of data corresponds to: • the value of the figure that’s in the central position, if the figures are odd numbers to the arithmetic mean of the figures that occupy the central position if the figures are even numbers.

45. The indices of central tendency have the limit of not giving us any info about the distribution of the data.

46. The students gather and elaborate some indices of dispersion and linear correlation

47. The range equals to Xmax-Xmin
2. INDICES OF DISPERSION
The indices of dispersion are numerical indicators that measure the variability of the data in a distribution of frequencies, they allow to evaluate briefly the distribution of data. Significant indices of dispersion are
The range equals to Xmax-Xmin
Average absolute deviation, the formula is
Variance, the formula is
Standard deviation which is the square root of the variance

48. Index of linear correlation with the formula of mixed moments The linear correlation allows you to compare two quantitative variables X and Y to study their grade of relation. The values of the index varies between -1 and +1; both the extreme values represent perfect relations between the variables, whereas 0 represents the absence of relation. This at least until we consider linear type relations. The formula used in the elaboration:

52. Interpretation of the results

53. 5^ phase The interpretation is the explanation of the survey conducted, it’s the phase in which you require mathematical skills to come to precise conclusions of the studied phenomenon. Note: the current phase needs in-depth analysis in the next UdA.

55. Last phase
Preparation of the self-evaluation questionnaire with the students.

56. The self-evaluation questionnaire