Summarizing the data. Graphical representationFor large data series information is easier to analyze when data is summarized into a frequency distributionA. Qualitative variables Frequency distribution obtained by counting the number of times each category occursExercise 1A group of 30 students are asked about their preference regarding the country they would prefer for following an Erasmus scholarship. The results of the survey are the following:1.France7.Italy13.Spain19.UK25.Spain

2.UK8.Spain14.UK20.Spain26.Germany

3.UK9.Spain15.UK21.France27.France

4.Germany10.UK16.France22.Germany28.France

5.UK11.Germany17.UK23.France29.UK

6.France12.France18.Italy24.UK30.Italy

Requests: Compute the frequency distribution Calculate the relative frequencies Make two graphical representations for the data: bar chart and structure diagram. If the University of Economics had available 100 Erasmus scholarships, how would you advice to distribute them among the 5 countries?

B. Quantitative discrete variables Frequency distribution obtained by counting the number of times each variant occurs Discrete variables have a limited number of possible variants.Exercise 2For a group of 40 families, a survey is conducting regarding the number of members of each family. The results are as follows:2; 3; 4; 2; 4; 3; 3; 1; 4; 3; 3; 3; 2; 2; 4; 4; 5; 1; 3; 2; 3; 3; 4; 2; 4; 1; 5; 1; 2; 3; 2; 4; 3; 3; 2; 3; 2; 3; 3; 3. Requests: Compute the frequency distribution Calculate the relative frequencies Make the graphical representations of the data What are the conclusions?C. Quantitative continuous variables

Steps in constructing a frequency distribution (group data on classes): Calculate the range of the date difference between the maximum and the minimum value in the data Decide upon the number of classes (based on the total number of observations in the data set) Calculate class/interval width ( for interval with equal width: divide the range by the number of classes) Determine the class/interval limits and construct the frequency distribution table Count observations and assign to classes compute absolute frequencies

Exercise 3

An analyst is collecting data for the salary of a companys employees. The data collected is as follows (expressed in RON): 1200, 2050, 1400, 2800, 1500, 2450, 1700, 2800, 1750, 1800, 1650, 1850, 1900, 1400, 1950, 2000, 2100, 2150, 2200, 1250, 2400, 3250, 2400, 2600, 2550, 2700, 1300, 2900, 2750, 3300. Requests: Group the data on 5 equal width intervals and form the frequency distribution table Compute the structure of the collectivity on the five intervals Plot the histrogram and the frequency polygon What is the percentage of employees with a salary greater than 2460?

Exercise 4For a series of 200 students, we know the structure of the collectivity regarding the grades obtained at an exam:GradeStructure of students (percentages)

510%

625%

735%

815%

910%

105%

What is the type of the variable?Determine the number of students from each category. Make a graphical representation of the data.