Leaving Certificate Statistics Vocabulary Booklet Name:________________________________ This Booklet Summaries Chapter 1 of Active Maths 4 Book 2 You must learn everything in this booklet and then refer back to your Active Maths book and exam papers to complete questions. Do not lose or misplace this Booklet.

 Statisticians are often faced with large of amounts of data.  When this data is summarised and presented to the public in the form of bar charts and pie charts.  This is called descriptive statistics

 Before an election people often try to predict who is going to win by asking people how they are going to vote.  When statisticians attempt to predict the outcome after analysing the data then this is called inferential statistics.

Data Categorical Data Ordinal Data Nominal Data Numerical Data Continuous Data Discrete Data

 Categorical Data: Questions that cannot be answered with numbers.  What colour are your eyes?  What’s your favourite song?  Numerical Data: Questions that can be answered with numbers.  How many films did you see last year?  What is your shoe size?

Ordinal Categorical Data: Data that can be ordered in some way. Obvious categories Nominal Categorical Data: Data that cannot be ordered in any way. Data using letters

 Ordinal (Ordered) Data:  Exam Results: A,B,C,D,E,F  Clothes sizes: S, M, L, XL, XXL  Nominal Data  Favourite band: U2, The Coronas, Coldplay, etc.

Are the following Ordinal or Nominal? 1. Favourite TV Programmes you Watch 2. Favourite Band 3. Grades in your Junior Certificate 4. Gender 5. Hair Colour 6. Favourite Soccer Player 7. Colours of the rainbow

Continuous Numerical Data: Data that can have any value inside some range. (Decimal Numbers) Discrete Numerical Data: Data that can only have a fixed number of values.(Whole Numbers) Data using numbers

 Examples:  How many students in the school?  How many books in your bag?  How many points did you score in the match?

Discrete  Marks  No. of scores  No. of coins  No. of goals scored by a team (cant have half a goal)  No of desks in this room We are dealing with whole numbers. 3, 7, 77, 800

 Example:  What height are you?  What weight are you?  How fast can you run 100 metres?

Continuous  Heights of students in class  Time  Speed of cars on a road  Time taken to run a hundred metre sprint  For example, Usain Bolt set the world record for the 100m running 9.58 Here we have decimal numbers. 1.66, 2.8, 0.33

Is this data Continuous or Discrete? 1. A random persons height 2. Time it takes to run a marathon 3. Amount of goals Robin van Persie scored last season 4. Amount of minutes played by Robin Van Persie last season 5. Number of Olympic medals won by Ireland 6. Number of number 1 singles by Rihanna 7. Temperature today

Primary Data  Primary Data is collected by an organisation or an individual who is going to use it.  Data you collect yourself.  Can you think of any methods on gaining primary data?

Primary Data  To collect Primary Data we can Carrying out:  Surveys  Questionnaires  Experiments  Observational studies

Secondary Data  Data which is available or has been collected by somebody else for a different purpose.  Data you look up in books or on the internet.  Examples??

Secondary Data  The Guinness book of world records,  The Census of Ireland.  Looking up the score for a match in a newspaper or online  Data from:  The internet  Data bases  Charts

 Who carried out the survey?  How was the sample chosen?  How was the population chosen?  What was the size of the sample?  What was the size of the population?

 What types of ways is there to collect data?  Survey  Questionnaire  Observational Studies  Designed Experiments

Steps in statistical investigation Pose a question Collect data Present and analyse the data Interpret the results (in light of the question)

 Univariate Data is when one item of information is collected.  Examples:  Colour of eyes  Distance from School  Height in centimetres

 Data that contains 2 items of information.  Examples:  The height and weight of a person.  Hours of study in a week and marks scored in an exam.  Colours of hair and Gender

Population  Population: the entire group that is being surveyed  Sample: a group that is selected at random from the population  Suppose you wanted to find out what teenagers favourite television show was. There is a school with 800 students in it.  But you only decide to interview 80 out of the 800

 When choosing a sample you must:  Ensure everybody has an equal chance of being selected  Ensure that the sample is random  In order for a sample to be reliable you must choose a sample that is large enough.

 Bias: a distortion of the results (may not give a clear picture)  If Bias exists the results will not give you a fair or accurate representation of the information  This happens when the sample is not random.

Avoiding Bias  Avoid Personal Questions and questions that people may not give an honest answer to. e.g. Where do you live? Are you well educated? Have you ever stolen?

Questionnaires  A questionnaire is a set of questions designed to obtain information from individuals  Two types: 1. Person (Interviewer) asks questions 2. People Given time to complete them on their own

 Avoid Leading Questions in Questionnaires:.  Do you think football players are overpaid? Yes____ No ____  Do you think students get too much homework? Yes ______ No______

 Avoid Bias or questions that may embarrass people or give dishonest answers in questionnaires.  Have you ever stolen from your local shop? Yes___ No___

 A simple random sample is selected in such a way that every person within the population has a equal chance of being selected.

 Stratified random sampling is where the population is divided into different subgroups where the people in each group share the same views and characteristics.  A simple random sample is then selected from these subgroups.

 A systematic random sample is a sample which is obtained by choosing people at regular intervals from an unordered list.  For example, suppose you wish to select 20 students from 200. Firstly, assign an individual number to each of the 200 students. Then select a Random number between 1 and 10 e.g. 7. Your sample of 20 students will then consist of the 7 th, 17 th, 27 th, 37 th student etc.

 Cluster sampling is where the population is divided into groups or clusters.  A number of these clusters are then selected and every person within that cluster is used to form the sample.

 Quota Sampling is where the person is given a group to sample on a question or topic. (E.g. men over 30, women over 60)  The person then selects whoever he wants from these groups to form his sample.

 Convenience sampling is simply where the sample is selected in the most convenient way possible.  Note:  Convenience and quota sampling are often unreliable and are prone to mistates and errors as the sample taken is not random.

 Mean (Average)  Mode (Most Common)  Median (Middle Number)

 Range (Highest - Lowest)  Interquartile Range  Standard Deviation

 Symmetrical Distribution:  For a symmetrical distribution the mean, mode and median are the same. Symmetrical distributions are often called the normal distribution

 In a skewed left distribution the Mean < Median < Mode

 In a skewed right distribution the Mean > Median > Mode

 An Outlier is a very high or very low value which is different from the other values in the set.  Example:  Your teachers age and your classes age.