DESCRIPTIVE STATISTICS Artur Wasiak

Table of contents definitions definitions Why do we use descriptive statistics? Why do we use descriptive statistics? method 1: steps of ploting histogram method 1: steps of ploting histogram method 2: calculating statistics method 2: calculating statistics summary summary questions questions

Definitions STATISTICS – mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data STATISTICS – mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data DESCRIPTIVE STATISTICS – statistical methods used to summarize or describe a collection of data DESCRIPTIVE STATISTICS – statistical methods used to summarize or describe a collection of data

The purpose Why do we use descriptive statistics? Why do we use descriptive statistics? This is aimed at making data legible. This is aimed at making data legible. Example… Example… 3,65,04,04,75,25,94,55,35,83,9 5,63,55,45,24,15,03,15,84,84,4 4,65,14,73,05,56,13,84,95,66,1 5,94,26,45,34,54,94,05,23,35,4 4,76,45,13,45,26,24,44,35,83,7 What do you think? Is it legible? How can we improve it? One of the possible ways - using graphical technics.

Frequency distribution (1) We first look for the lowest and the highest values in the sample. We first look for the lowest and the highest values in the sample. 3,65,04,04,75,25,94,55,35,83,9 5,63,55,45,24,15,03,15,84,84,4 4,65,14,73,05,56,13,84,95,66,1 5,94,26,45,34,54,94,05,23,35,4 4,76,45,13,45,26,24,44,35,83,7

Frequency distribution (2) We want to divide the data into a few groups called „classes”. We want to divide the data into a few groups called „classes”. In our example 7 classes is an appropriate number. In our example 7 classes is an appropriate number. number of class boundariesmid-valuefrequency 1 2,95 – 3,45 3,2? 2 3,45 – 3,95 3,7 3 3,95 – 4,45 4,2 4 4,45 – 4,95 4,7 5 4,95 – 5,45 5,2 6 5,45 – 5,95 5,7 7 5,95 – 6,45 6,2

Frequency distribution (3) 3,6 (2) 5,0 (5) 4,0 (3) 4,7 (4) 5,2 (5) 5,9 (6) 4,5 (4) 5,3 (5) 5,8 (6) 3,9 (2) 5,6 (6) 3,5 (2) 5,4 (5) 5,2 (5) 4,1 (3) 5,0 (5) 3,1 (1) 5,8 (6) 4,8 (4) 4,4 (3) 4,6 (4) 5,1 (5) 4,7 (4) 3,0 (1) 5,5 (6) 6,1 (7) 3,8 (2) 4,9 (4) 5,6 (6) 6,1 (7) 5,9 (6) 4,2 (3) 6,4 (7) 5,3 (5) 4,5 (4) 4,9 (4) 4,0 (3) 5,2 (5) 3,3 (1) 5,4 (5) 4,7 (4) 6,4 (7) 5,1 (5) 3,4 (1) 5,2 (5) 6,2 (7) 4,4 (3) 4,3 (3) 5,8 (6) 3,7 (2)

Frequency distribution (4) number of class boundariesmid-valuefrequency 1 2,95 – 3,45 3,24 2 3,45 – 3,95 3,75 3 3,95 – 4,45 4,27 4 4,45 – 4,95 4,79 5 4,95 – 5,45 5, ,45 – 5,95 5,78 7 5,95 – 6,45 6,25

Histogram Using values from the table, we can prepare the histogram. Using values from the table, we can prepare the histogram.

Frequency polygone Connecting midpoints of the horizontal segments in histogram, we obtain frequency polygone. Connecting midpoints of the horizontal segments in histogram, we obtain frequency polygone.

Calculating statistics (1) This is the second method of summarising information contained in the data. This is the second method of summarising information contained in the data. We can calculate statistics which characterise some basic features of the sample. The most frequently used statistics are: arithmetical mean, variance and standard deviation, median. We can calculate statistics which characterise some basic features of the sample. The most frequently used statistics are: arithmetical mean, variance and standard deviation, median.

Calculating statistics (2) Calculating arithmetical mean: Calculating arithmetical mean: A) using raw material (sum of 50 numbers) / 50 = 4,85 A) using raw material (sum of 50 numbers) / 50 = 4,85 B) using frequency distribution (4*3,2 + 5*3,7 + … + 5*6,2) / 50 = 4,84 B) using frequency distribution (4*3,2 + 5*3,7 + … + 5*6,2) / 50 = 4,84

Summary Descriptive statistics is the first step of analysis of the collected data. Descriptive statistics is the first step of analysis of the collected data. There are two methods: graphical technics and calculating statistics. There are two methods: graphical technics and calculating statistics. In both of them we concede some details to make the whole set of data legible. In both of them we concede some details to make the whole set of data legible.

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