Chapter 3

Question 1

What is an array ?

Answer 1

A data set that has been sorted from smallest to largest

Question 2

What is ungrounded data ?

Answer 2

Observations that are not arranged in classes or groups

Question 3

Frequency density ?

Answer 3

Differs from place to place on the definition region; which means that there could be more data points concentrated over certain intervals than others

• it is of some importance when it comes to resenting the distribution of the data graphically over the aforementioned definition region

Question 4

What is frequency ?

Answer 4

The number of observations within a particular class

Question 5

What is a frequency table ?

Answer 5

A table with classes of values and corresponding frequencies

• this table indicates vow densely the observed data is distributed over the different classes (intervals) ~ which motivates the term frequency distribution

Question 6

How is a frequency table set ?

Answer 6

When one sets a frequency table up for continuous data, one must first divide the region of variation(the data region) into a number of logically determined intervals and then one counts how many observations fall within these intervals

Question 7

What is the range ?

Answer 7

The difference between the largest and smallest observations

Question 8

What happens if there are too few classes of data or too many classes of data ?

Answer 8

• If too few classes are used then information is lost because all the observations will be concentrated within the very few classes
• If too many classes are used then the data points are too sparsely distributed among the classes

= both these problems thwart one’s ability to make meaningful conclusions for the data

Question 9

What is Sturge’s rule (useful rule of thumb) ?

Answer 9

k, the number classes is a frequency table, can be determined by the formula : k= 1 + 1.4ln(n), where n is the number of observations in the data set and k is rounded of to the nearest whole number

Question 10

How is the class’ width calculated ?

Answer 10

It is calculated by dividing the range by the number of classes

Question 11

Class boundaries ?

Answer 11

• the lowered boundary of the first class must be less than or equal to the smallest observation
• class boundaries must clearly distinguish intervals- there must be no doubt as to where a value lies

Question 12

What is class midpoint?

Answer 12

The centre of each class

Question 13

What is cumulative frequency(F)?

Answer 13

The cumulative frequency of post x os the number observations in a data set with values smaller than x

Question 14

What is relative frequency(r)?

Answer 14

The frequency(f) divided by the total number of observations in a data set

Question 15

What is percentage frequency?

Answer 15

The relative frequency multiplied by 100

Question 16

What is relative cumulative frequency(R)?

Answer 16

Cumulative frequency(F) divided by the total number of observations in the data set(n)

Question 17

What is percentage cumulative frequency?

Answer 17

The relative cumulative frequency multiplied by 100

Question 18

What is grouped data?

Answer 18

Data divided into classes

Question 19

What are the techniques to graphically represent continuous data ?

Answer 19

• Dot plots
• Histogram
• Frequency polygon
• cumulative frequency polygon .
• relative frequency polygon

Question 20

What is a scatter diagram ?

Answer 20

A simple way of representing data if the dataset is relatively small

• it indicates how the data is distributed across the various possible values

Question 21

What is a Histogram?

Answer 21

A graphical representation of a frequency table

Question 22

What is a frequency polygon?

Answer 22

A graph where the frequencies of each class interval are plotted against the class mid-points of the corresponding class interval and then the points are joined with straight lines

• two class intervals or f=0 are added above and below

Question 23

What is a cumulative frequency polygon ?

Answer 23

A graphical representation of a cumulative frequency table

Question 24

What is a relative frequency polygon ?

Answer 24

A frequency polygon that uses relative frequencies
Is a graphical representation of the relative frequency table

• the area below the relative frequency polygon is equal to 1

Question 25

Remark ?

Answer 25

• if the sample is reasonably large, then the literature says that the relative frequency polygon obtained from a randomly chosen sample is approximately the same as the relative frequency polygon obtained from the whole population from which the original sample was taken. The same can be said about the relative cumulative frequency polygon

Question 26

What are the graphical representations of discrete data ?

Answer 26

• Dot plots
• Bar charts
• Pie charts

Question 27

What is a pie chart ?

Answer 27

A circle or sector chart that graphically represents proportions by means of a circle that is subdivided into sectors so that the areas of these sectors correspond with percentages

• Draw a circle
• calculate that angles of the sectors by r×360° , with r being the relative frequency