What is Statistic?

  • Statistics: Statistics can be described as the science of classifying and organizing data in order to draw inferences. The collection and organization of data is usually called descriptive statistics; the process of deciding what conclusions may be reached is called inferential statistics.

Example 1: What did we see on television last night?

We take 8 friends of the our school, and we ask them for the program of television they saw last night. We are doing a statistical study with these datas:

With these datas, we obtain the following pie chart. This pie chart shows what we friends saw the last night on television:


The term data refers to the set of values, elements or numbers under consideration.

Population Sample
It is the complete set of all observations pertaining to a single characteristic of interest.    It is the set of values that are actually collected in the course of an investigation.   

Example 2.

In the last example, in our school there are more than eigth persons, but we haven´t enough time to ask all of them for the program of tv they saw last night, for this reason, we only ask to eight friends.

In this example, the population are all pupils of our school, and the sample are our eigth friends.

Population and sample

Quantitative data discrete and continous.

Quantitative data discrete Quantitative data continuous
The values are in integers (whole numbers), for example the number of person that are seen the television, the numbers of the lotery, etc. The values are in numerical measurements, for example the weight, the temperature, the size, etc.

Quantitative data continuous

        In this case we group together observations that have valous close to each other so that instead of having a large number of values, each with a small number of observations, we have a smaller set of intervals, each containing a larger number of observations. We group these data by dividing the interval of numbers that contains all the values of the data into smaller intervals, called classes. The interval of values in each case is called a class. The class limits are the highest and lowest values specified for each class. The center of an interval, called class mark, is equal to half the sum of the class limits.

Frequency and relative frequency

Frequency (f_i) Relative frequency (h_i)
The frequency (f_i) of a value is the number of times the value occurred in our study. The relative frequency (h_i) of a value is equal to the number of observations(frequency) divided by the total number of observations N (total frequency), ie,          h_i = f_i / N.

Example 3: height in the classroom.

We know the height of 40 pupils of a school, and we put these height in a table:

The average.

The average of a set of n values x_1, x_2, x_3, ...x_n is the sum of these values divided by the number of values, n.

  • For qualitative data discrete:

overline{x} = sum{i=1}{n}{x_i h_i}   =    {sum{i=1}{n}{x_i f_i}}/N, where f_i is the frequency, h_i is the relative frequency and N is the total number os observations.          (N = sum{i=1}{n}{f_i}).

Example 4: the cards in the soccer.

We will do a study of the yellow and red cards that the referees have showed in 15 matchs of a league of soccer. We know the following results:


NOTE: f_i is the number of matchs of whom the referee showed x yellow (or red) cards in each match.

1.-What is the average of yellow cards in each match in the league of soccer?

overline{x} = (3•4+5•3+6•5+ 10•3)/15 = 5.8
ie, the referee have showed 5.8 yellow cards in each match in the league, of average.

2.-What is the average of red cards in each match in the league of soccer?

overline{x} = (7•0+5•1+2•3+1•4)/15 = 1.4
ie, the referee have showed 1.4 red cards in each match in the league, of average.

  • For qualitative data continous we take the variable value as the class mark.

Example 5: the babys.

We know the weight of 100 babys, and we put in the following table:

The average is:
overline{x} = (2.25+2.75 •17+3.25 •55+3.75 •19+4.25 •7+4.75)/100 = 3.34 Kg.


statistical.txt · Última modificación: 24/04/2017 13:13 (editor externo)
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