Chapter 3 Flashcards
What is an array ?
A data set that has been sorted from smallest to largest
What is ungrounded data ?
Observations that are not arranged in classes or groups
Frequency density ?
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
What is frequency ?
The number of observations within a particular class
What is a frequency table ?
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
How is a frequency table set ?
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
What is the range ?
The difference between the largest and smallest observations
What happens if there are too few classes of data or too many classes of data ?
- 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
What is Sturge’s rule (useful rule of thumb) ?
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
How is the class’ width calculated ?
It is calculated by dividing the range by the number of classes
Class boundaries ?
- 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
What is class midpoint?
The centre of each class
What is cumulative frequency(F)?
The cumulative frequency of post x os the number observations in a data set with values smaller than x
What is relative frequency(r)?
The frequency(f) divided by the total number of observations in a data set
What is percentage frequency?
The relative frequency multiplied by 100
What is relative cumulative frequency(R)?
Cumulative frequency(F) divided by the total number of observations in the data set(n)
What is percentage cumulative frequency?
The relative cumulative frequency multiplied by 100
What is grouped data?
Data divided into classes
What are the techniques to graphically represent continuous data ?
- Dot plots
- Histogram
- Frequency polygon
- cumulative frequency polygon .
- relative frequency polygon
What is a scatter diagram ?
A simple way of representing data if the dataset is relatively small
- it indicates how the data is distributed across the various possible values
What is a Histogram?
A graphical representation of a frequency table
What is a frequency polygon?
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
What is a cumulative frequency polygon ?
A graphical representation of a cumulative frequency table
What is a relative frequency polygon ?
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
Remark ?
- 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
What are the graphical representations of discrete data ?
- Dot plots
- Bar charts
- Pie charts
What is a pie chart ?
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
