chapter one (stat 160)

Chapter I : Describing Data With Graphs

Kian Jahromi

May 31, 2012

Kian Jahromi () Chapter I : Describing Data With Graphs May 31, 2012 1 / 19

Table of contents

1 VARIABLES AND DATATYPES OF VARIABLES

2 GRAPHS FOR CATEGORICAL DATA

3 GRAPHS FOR QUANTITATIVE DATA

4 Interpreting Graphs with a Critical Eye


VARIABLES AND DATA

Definitions

Definition

A Variable is a characteristic that changes or varies over time and/or fordifferent individuals or objects under consideration.

Definition

An experimental unit is the individual or object on which a variable ismeasured. A single measurement or data value results when a variable isactually measured on an experimental unit.

Definition

A population is the set of all measurements of interest to the investigator.

Definition

A sample is a subset of measurements selected from the population ofinterest.


VARIABLES AND DATA

Example

Identify the experimental units on which the following variables aremeasured:a. Gender of a studentThe studentb. Number of errors on a midterm examThe midterm examc. Age of a cancer patientThe patiente. Colour of a car entering a parking lotThe Car


VARIABLES AND DATA

Definition

Univariate data result when a single variable is measured on a singleexperimental unit.

Definition

Bivariate data result when two variables are measured on a singleexperimental unit. Multivariate data result when more than two variablesare measured.


VARIABLES AND DATA

The following data set is a multivariate data set. Each column itself is aUnivariate data set.


VARIABLES AND DATA TYPES OF VARIABLES

Definition

Qualitative variables measure a quality or characteristic on eachexperimental unit. Quantitative variables measure a numerical quantityor amount on each experimental unit.

Definition

Definition A discrete variable can assume only a finite or countablenumber of values. A continuous variable can assume the infinitely manyvalues corresponding to the points on a line interval.


GRAPHS FOR CATEGORICAL DATA

Graphs for Categorical Data

After the data have been collected, they can be consolidated andsummarized to show the following information:

(i) What values of the variable have been measured

(ii) How often each value has occurred For this purpose, you canconstruct a statistical table that can be used to display the

Example

A bag contains 25 candies:



So, the Statistical table for last page example is as follows:

Also, it is possible to express the frequency of each categories usingfollowing formulas:

(i) Relative frequency= frequencyn (n is the total number of

measurements)(ii) Percent= 100 × Relative frequency

The following table contain the relative frequency and percent for eachcategories of last example:



Example

Fifty people are grouped into four categories A, B, C, and D and thenumber of people who fall into each category is shown in the table:

The following figure is the bar chart for upper table:



and the pie chart is as follows:


GRAPHS FOR QUANTITATIVE DATA


Line ChartsWhen a quantitative variable is recorded over time at equally spacedintervals (such as daily, weekly, monthly, quarterly, or yearly), the data setforms a time series. Time series data are most effectively presented on aline chart with time as the horizontal axis. The idea is to try to discern apattern or trend that will likely continue into the future, and then to usethat pattern to make accurate predictions for the immediate future.

Example



DotplotsMany sets of quantitative data consist of numbers that cannot easily beseparated into categories or intervals of time. You need a different way tograph this type of data! The simplest graph for quantitative data is thedotplot. For a small set of measurements for example, the set 2, 6, 9, 3, 7,6 you can simply plot the measurements as points on a horizontal axis.

Example



Stem and Leaf PlotsAnother simple way to display the distribution of a quantitative data set isthe stem and leaf plot. This plot presents a graphical display of the datausing the actual numerical values of each data point.How Do I Construct a Stem and Leaf Plot?

1. Divide each measurement into two parts: the stem and theleaf .

2. List the stems in a column, with a vertical line to their right.

3. For each measurement, record the leaf portion in the samerow as its corresponding stem.

4. Order the leaves from lowest to highest in each stem.

5. Provide a key to your stem and leaf coding so that thereader can recreate the actual measurements if necessary.



Example


Interpreting Graphs with a Critical Eye

Definition

A distribution is symmetric if the left and right sides of the distribution,when divided at the middle value, form mirror images.

Definition

A distribution is skewed to the right if a greater proportion of themeasurements lie to the right of the peak value. Distributions that areskewed right contain a few unusually large measurements.


Interpreting Graphs with a Critical Eye

Definition

A distribution is skewed to the left if a greater proportion of themeasurements lie to the left of the peak value. Distributions that areskewed left contain a few unusually small measurements.

Definition

A distribution is unimodal if it has one peak; a bimodal distribution hastwo peaks.Bimodal distributions often represent a mixture of two differentpopulations in the data set.


chapter one (stat 160)

Technology

type of data

data point

data setforms

multivariate data set

aunivariate data set

time series data

multivariate data result

denitionbivariate data