Chapter 3 Graphical Descriptive Techniques 2

Question 1

What is a class?

Answer 1

A group that covers a range of observations

Classes:
1-10
11-20
21-30 etc.

Question 2

How is the range of classes calculated

Answer 2

Since the lowest and highest values must be included. The classes will be based off how to partition up the ranges in-between these two extremes.

Question 3

What is a histogram?

Answer 3

A histograms is created by drawing rectangles whose bases are the intervals and whose heights are the frequncies

Question 4

What is Sturge’s formula

Answer 4

A formula that recommends the number of class intervals to use

Number of class intervals = 1 +3.3 log (n)
n = number of observations

This is just a guideline however, sometimes there is a better method dependent on the context

Question 5

How do we determine the class interval widths

Answer 5

Class width = (Largest Observation - Smallest Observation) / Number of Classes

This is just a guideline however, sometimes there is a better method dependent on the context

Question 6

What are the 4 characteristics used to describe the shape of histograms?

Answer 6

Symmetry (a histogram is said to be symmetric if, when we draw a vertical line down the center of the histogram, the two sides are identical in shape and size)

Skewness (a histogram with a long tail extending either to the right or left, positively skewed has a higher distribution on the left while a negatively skewed diagram has a higher distribution the right

Number of Modal Classes, (can be unimodal or bimodal dependent on the number of peaks present)

Bell Shape (special type of symmetric unimodal histogram that is bell shaped (high frequency near the middle)

Question 7

What does Skewness refer to when positive and negative is mentioned

Answer 7

The skew of the top of the graph either is positive (moves up on the X axis) therefore implying that there is higher frequency on the left side of the diagram. Whilst a negative skew (moves down on the X axis) implies that there is a higher frequency on the right side of the diagram

Question 8

What is a mode

Answer 8

The observation that occurs with the greatest frequency

Question 9

What is a modal class

Answer 9

The class with the largest number of observations

Question 10

Factors that Identify when to use a histogram

Answer 10

Objective: Describe a single set of data
Data type: Interval

Question 11

What is cross-sectional data

Answer 11

Observations are measured at the same time

Question 12

What is time-series data

Answer 12

Observations are measured at successive points in time

Question 13

What chart is often used to depict time-series data

Answer 13

A line chart

Question 14

What is a line chart

Answer 14

A chat that plots the variable over time

Question 15

What is a scatter diagram

Answer 15

A graph representing data that has two variables (usually X for the independent variable, and Y for the variable that is dependent on X)

Question 16

What is a linear relationship

Answer 16

If we draw a straight line through the points in such a way that the line represents the relationship (using the least squares method). If most points fall close to the line we could that there is a Linear Relationship

Question 17

What is it called when one variable increases when the other does

Answer 17

Positive linear relationship

Question 18

What is it called when two variables tend to move in opposite directions

Answer 18

Negative linear relationship

Question 19

Remember Correlation is not causation

Answer 19

However there is some level of connection there

Question 20

Factors that Identify when to use a scatter diagram

Answer 20

Objective: Describe the relationship between two variables
Data type: Interval

Question 21

What is graphical excellence

Answer 21

A term applied to techniques that are informative and concise and that impart information clearly to their viewers

Question 22

What is graphical deception

Answer 22

A term applied to techniques that are not informative and concise and impart incorrect information to their viewers

Question 23

The 5 characteristics of Graphical Excellence

Answer 23

The graph present large data sets concisely and coherently

The ideas and concepts the statistics practitioner wants to deliver are clearly understood by the viewer

The graph encourages the viewer to compare two or more variables

The display induces the viewer to address the substance of the data and not the form of the graph

There is no distortion of what the data reveals

Question 24

What are some methods in graphing used to deceive

Answer 24

Graphs without Scale

Graphs with Different Captions

The shrinking or elongating of the x axis to adjust the slope of the line

Graphs showing considerable swings or relative stability by adjusting the x axis

Bar graphs where the size of the bar on the x axis is made proportional to its height thus adding more size to it (also works with pictograms)