Data analysis with graphs

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Used to report on a wide variety of variables including prices and wages, ultraviolet levels in sunlight and even the readability of textbook

Researchers, advertisers, professors and sport announcers all use statistics

Frequency polygon

illustrate the same information as a histogram or bar graph

Histogram

Example: weights, temperature or travel time

They are used for variables whose values can be arranged in numerical order

Specials form of bar graph. The bar in a histogram are connected and represent a continuous range of values

Intevals

convenient to use from 5 to 20 equal intervals that cover the entire range from smallest to largest

When the number of values is large, data are usually grouped into classes or intervals

Continuous variable

Example: Hight of a student in your school

Value within given range

Discrete variable

Example: number of students in each class

certain separate values

Data analysis with graphs

Statistics Concept Map

Measures of Central Tendency

Outliers

values distant from majority of the data

Mode

Some distributions do not have mode while others have several

the value that occurs most frequently in a distribution

Median

Middle value of the data when they are ranked highest to lowest

Mean

Mean is also known as average

defined as the sum of the value of a variable divided by the number of values

Used to summarize a set of data

Bias in Surveys

Response Bias

This occurs when participants in a survey deliberately give false answers

Measurement Bias

This occurs when the data collected method consistently either under or overestimates a characteristics of the population

Non Response Bias

This occurs when particular group are under represented in a survey because they choose not to participate

Sample Bias

This occurs when the sampling frame does not reflect the characteristics of the population

Sampling Techniques

Convenience Sample

Sample is selected because it is easily accessible

Voluntary Response Sample

The researchers simply invites any member of the population to participate in the survey

Multi Stage Sample

Example: population consisted of all Ontario households, you could first randomly sample all cities and townships then sample all subdivisions or blocks then finally sample from all the houses

Uses several levels of random sampling

Cluster Sample

Examples: Fast food chain could save time and money by severing all its employees at random selected locations instead of surveying randomly selected employees throughout the chain

If certain groups are likely to be represent of the entire population, you can use a random selection of such groups as a cluster sample

Stratified Sample

Has the same proportion of members from each stratum as the population

group of members who share common characteristics

Example: Gender, age, education level, etc

Systematic Sample

You go through the population sequentially and select members at regular intervals

Simple Random Sample

Select names by drawing names randomly or by assigning each member with a number then using a random number generator to pick

Every member has an equal chance of being selected and the selection of any particular individual does not affect the chance of others

Sampling frame

The group of individuals who actually have a chance of being selected

Population

Example students in your school

Refers to all individuals who belong to a group being studied

Indices

Readability index

used to estimate the years of schooling required to read the material easily

Gunning fog is a measure of readability index

Consumer price index

consumer price index and cost of living index are not the same

Inflation

Increases in price which corresponds to a decrease in the value of money

Most widely reported of these economic indices

Time series graph

Used to show how indices change overtime

Index

The base level is set so that the index produces number that are easy to understand and compare

relates the value of a variable to base level which is often the value on a particular data

Another way to summarize data and recognize trends

pictographs

Circle graphs

often used instead of bar graph to illustrate categorial data

Categorical data

Example: surveys of blood types, citizenship, favorite foods

Given Labels rather than being measured numerically

Relative frequency

Shows the frequency of a data group as a fraction or percent of the whole data set

Bar graph

Classes

Raw Data

Frequency diagram

Frequency table

gives an overview of the distribution of values of the variable and reveal trends in a data

Variable

Variable is the quantity that is being measured

Raw data is the unprocessed information collected for a study

Statistics

Statistics is gathering, organization, analysis and presentation of numerical information