Unit 1: Representing Data & Analysing 2D Data 1.1 Visual Displays of Data

Visual Displays of Data Use the appropriate display for particular data Types of Data Quantitative (numerical) Qualitative (categorical) Discrete Continuous OrdinalNominal

Types of Variables Qualitative –Cannot be measured numerically –Ex: eye colour, opinion –height, distance, mass, time, age, number of moles Quantitative/Numerical –can be measured numerically –Ex:

Types of Quantitative Variables Discrete –Can be described with whole numbers –Ex: number of students, pairs of shoes, number of absences heights of students, length of time a plant takes to germinate Continuous –There is a continuum of possible values –Ex:

Name that Data Type Age Favourite meal Television viewing preference Volume of radio Seating capacity Quantitative discrete (could be continuous) Qualitative Quantitative continuous Quantitative discrete

Types of Qualitative Data Also called categorical Data can be grouped by specific categories Ordinal: naturally ordered –E.g. height (short, average, tall), opinion (poor, satisfactory, good, excellent) Interval: each category represents equal amount of time Nominal: no natural order –E.g. hair colour, subject

Bar Charts Most effective when you wish to emphasize individual items Can be used with ordinal or nominal data

Pie Charts Shows frequency distribution Can be used for qualitative or quantitative data Needs a legend and scale

Line Graphs Suggests trends and patterns Change implied as you move from one item to next Should only be used to link data points along interval scale Time most common interval

Additional Graphs Stem-and-leaf plot –Good for seeing frequencies of individual items –Measures of central tendency Pictograph –Shows frequency distributions –All pictures should be the same size –Needs legend (e.g.  = 1 club)

All Graphs Need Title Labelled axes Scale –Qualitative: Nominal categorical, interval categorical, ordinal categorical Legend (pie chart, pictograph)

Identifying Numerical And Categorical Scales Identify the categorical scale and the numerical scale. Mathematically, does it make sense to connect the data points by a line? Why or why not? How much useful information would be provided if either the categorical or numerical scale where missing? Numerical Categorical Not much! We can’t really tell anything about the graph. Yes: trend lines, and each grade represents an equal interval of time

Classifying Categorical Scales Nominal Categorical Scale Line graph inappropriate Bar graph appropriate

Classifying Categorical Scales Interval Categorical Scale Line graph appropriate Bar graph appropriate

Classifying Categorical Scales Interval Categorical Scale (each grade represents an equal amount of time) Line graph appropriate Bar graph appropriate With interval scales, you may use line graphs or bar graphs – it depends on what you want to emphasize

Classifying Categorical Scales Ordinal Scale Line graph inappropriate Bar graph appropriate

Split-Bar Graphs Used to compare information in which two or more different quantities are represented by the length of the bars Who sold more, East or West? Who had the best quarter, relative to their total sales?

East: = 105 West: (50-20) + (65-25) + (55-40) + (51-20) = 116 Therefore, West sold more, in terms of raw numbers. Percentage-wise: East: 40 = 38% ____ 105 West: 40 = 34% ____ 116 Therefore, East had the relatively best quarter.