Descriptive Statistic Part I Laura Portell 1 Introduction What happened Why did it happen What will happen How to make it happen Descriptive analytics Diagnostic analytics Predictive analytics Prescriptive analytics 2 What is Statistics Statistics is a branch of mathematics dealing with obtaining ordering and analyzing a set of data in order to obtain explanations and predictions about observed phenomena Statistics converts data to information You can take decisions and actions 3 Basic Statistical Terms Population Sample Individual 4 The study of statistics can be categorized into two main branches Statistics Branches Descriptive statistics Inferential statistics 5 Statistics Branches Descriptive statistics A descriptive statistic is a summary statistic that quantitatively describes or summarizes features from a collection of information Descriptive statistics is used to collect store order make tables or graphs and calculate basic parameters on the data set 6 Statistics Branches Inferential statistics Inferential statistics takes data from a sample and makes inferences about the larger population from which the sample was drawn Draw conclusions from a sample and generalize them to a population 7 Example You can stand in the middle of the street and ask 100 people how many trips in a week they do by public transport their own vehicle or on foot means of transport public transport vehicle foot 1 4 8 10 2 0 20 2 people 3 5 5 5 4 2 0 15 8 Example Descriptive statistic Mean for each type of transport and bar chart Inferential statistic statistical study population are more likely to travel by public transport than by their own vehicle 9 Statistics Branches Summary Statistic Descriptive Inferential Collects and organizes data presents it informatively Makes estimates and hypotheses is based on probabilities 10 Data 1 100 50 20 11 Qualitative Data vs Quantitative Data Most data can be put into the following categories Qualitative or Quantitative Qualitative Data Quantitative Data Definition Qualitative data are the result of categorizing or describing attributes of a population Qualitative data are generally described by words or letters Quantitative data are the result of counting or measuring attributes of a population Quantitative data are always numbers Examples Blood type Ethnic group Population density Number of students who take descriptive analytics 12 Discrete Data vs Continuous Data Quantitative data may be either Discrete or Continuous Discrete Data Discrete data is just data that cannot be broken down into smaller parts This type of data consists of integers positive and negative numbers e g 100 10 100 and so on and is finite meaning it reaches a limit Continuous Data Continuous data is data that can be infinitely broken down into smaller parts or data that continuously fluctuates 13 Levels of Measurement Levels of measurement tell you how precisely variables are recorded In descending order of precision the four different levels of measurement are Nominal In this level of measurement the numbers in the variable are used only to classify the data into categories In this level of measurement words letters and alpha numeric symbols can be used ex Variable that classifies in gender categories female gender as F male gender as M and transgender as T 14 Levels of Measurement Ordinal This level of measurement depicts some ordered relationship among the variable s observations ex Variable that measures the quality of a bus trip The variable can take integer values from 1 to 5 where the value 1 is the worst and 5 is the best 15 Levels of Measurement Interval Interval Scale is defined as a numerical scale where the order of the variables is known as well as the difference between these variables This data type is always numeric and the value zero does not indicate the absence of the property ex 80 degrees is always higher than 50 degrees and the difference between these two temperatures is the same as the difference between 70 degrees and 40 degrees 16 Levels of Measurement Ratio In this level of measurement the observations in addition to having equal intervals can have a value of zero as well ex Variable that quantifies the salary of a person If one person earns 20 and another earns 10 the first person earns more than the second The value 0 indicate the absence of property 17 Descriptive Statistic 18 Descriptive statistic Descriptive statistics summarize and organize characteristics of a data set There are 3 main types of descriptive statistics The distribution frequency of each value The central tendency averages of the values The variability or dispersion how spread out the values are 19 Descriptive statistic Distribution Frequency or absolute frequency f Number of times the observation occurred in a study Absolute frequency is usually expressed as a whole number Relative frequency h Ratio of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes 20 Descriptive statistic Distribution Percentage frequency p Display of data that specifies the percentage of observations that exist for each data point or grouping of data points Percentage frequency frequency of the class n 100 relative frequency 100 Cumulative frequency A cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution You re adding up a value and all of the values that came before it 21 Example Distribution We ask 10 people how many people do you live with at home 1 0 3 2 2 3 1 3 3 1 Absolute frequency Cumulative absolute frequency Fi Relative frequency hi Cumulative relative frequency Hi Percentage frequency pi Cumulative percentage frequency Pi 0 1 2 3 1 3 2 4 1 4 6 10 0 1 0 3 0 2 0 4 0 1 0 4 0 6 1 10 30 20 40 10 40 60 100 22 Descriptive statistic Central tendency Measures of central tendency estimate the centre or average of a data set Mean Mean is the average of all the observations Mean is defined as the sum of all the observations divided by the total number of observations 23 Descriptive statistic Central tendency Median The value of the middlemost observation obtained after arranging the data in ascending order is called the median of the data If the series has an even number of scores the median is the mean between the two If the series has an odd number of measures the median is the central score of the central scores series Mode Mode is defined as the most frequent or common observation occurring in a