C4: Graphical Techniques

Question 1

Data

Answer 1

= a set of specific values observed in an experiment.

- comprises of a sample.

Question 2

Sample

Answer 2

= sub-set collected from a popn.

• used to deduce some properties about the sample space.

Question 3

Statistical methods

Answer 3

Methods that enable us to look at information from a small collection of subjects/samples & make deductions about a larger collection of subjects/popn.

Question 4

Individuals

Answer 4

Subjects/objects included in the study.

Question 5

Descriptive statistics

Answer 5

Branch of statistics that deals with the organising & presenting of data.

Question 6

Variable

Answer 6

A characteristic of the individual to be measured/observed.

Question 7

Types Of Variables(2)

Answer 7

[A] Quantitative variable
= has a numerical measurement for which arithmetic operations makes sense.

[B] Qualitative variable
= describes an individual by placing an individual into a category/group.

Question 8

Data sources

Answer 8

Where data is obtained.

Question 9

Types Of Data(2)

Answer 9

[A] Population data
= data are from every individual of interest.
• popn parameter = numerical measure that describes an aspect of a popn.

[B] Sample data
= data are from only some of the individuals of interest.
• sample statistic = numerical measure that describes an aspect of a sample.
• varies from sample to sample.
• incomplete.

Question 10

Raw data

Answer 10

Collected data that hasn’t been organized numerically in any way.

Question 11

Array

Answer 11

An arrangement of raw data either in ascending or descending order of magnitude.

Question 12

Scales Of Measurements(4) NOIR

Answer 12

[A] Nominal scale
= measures type of data that consists of names/labels/categories.
• order is not important.
eg. Eye colour.

[B] Ordinal scale
= categorized data that can be ordered/ranked.
• given positions from smallest to largest.
• differences between data values indeterminate & meaningless.
eg. Grades.

[C] Interval scale
= applies to data that can be arranged in order.
• difference between data values is meaningful.
eg. Temperature.

[D] Ratio scale
= data that can be arranged in order.
• differences between values & ratios of data values are meaningful.
• data at ratio level

Question 13

Qualitative data

Answer 13

Nominal & Ordinal

Question 14

Quantitative data

Answer 14

Interval & Ratio

Question 15

Data collection

Answer 15

The methods used to obtain pertinent information from the elementary units drawn into a sample.

Question 16

Approaches To Data Collection(3) DIE

Answer 16

[A] Direct observation
• done by asking questions.
• gives more accurate information.
eg. Human populations.

[B] Interview methods
• similar if not number 1.

[C] Experimentation.

Question 17

Terminology: Graphical methods

Range

Answer 17

Difference between the largest value and smallest value of the data set.

Question 18

Cluster

Answer 18

A group of points that fall very close together.

Question 19

Outlier

Answer 19

An observation that’s usually far from the rest of the data.

Question 20

Relative frequency

Answer 20

= A proportion of the data having a certain property.

• gives the proportion of the observations falling in a particular group.

Question 21

Frequency distribution

Answer 21

= an arrangement of data that allows the frequency of the occurrence of the values in each of several size classes.
• simplifies data without losing too many details.

Question 22

Plot Types(7) DPB2LSH

Answer 22

• Dot plot.
• Pie chart.
• Box plot.
• Bar graph.
• Line graph.
• Stem & Leaf plot.
• Histogram.

Question 23

Dot plot

Answer 23

= plot of a batch of no. on a vertical or horizontal scale.
• each no. = a dot.
• dots should be distinct.

Question 24

Pie charts

Answer 24

= a circle divided into segments.
• size of each segment proportional to the importance of data category of random variable relative to the whole.
• used for categorical data —> ordinal scale.

Question 25

Bar graph

Answer 25

= a simple presentation of the categorical/discrete data via bars put side to side.
• bars should be of same thickness.

Question 26

Line graph

Answer 26

= graph used to show the value of a random variable over time.
• used to investigate trends in 2 variables which are related.

Question 27

Stem & Leaf plot

Answer 27

= a method of EDA(Exploratory Data Analysis) used to ran-order and arrange data into groups.
• good for plotting data with many observations (~ 15-50).
• numbers are split into 2 parts: stem & leaf.
• has a key.
• displays shape of the data distribution.
• shows us all data (in array format).
• helps us to spot cluster data values.
☆ when stem has too many leaves, split the stem into 2 or more line.

Question 28

Histogram

Answer 28

• constructed from frequency table.
• bars are continuous.
• x-axis –> intervals.
• y-axis –> no. of scores in each interval is height of a rectangle.
• used for continuous variables & discrete variables.
• shape varies.
• shows distributional aspects of a continuous variable (symmetry + slowness of the data).

Question 29

Histogram Types(2)

Answer 29

• Equal width Histogram.

* Unequal width Histogram.

Question 30

Histogram Interpretation

Answer 30

• bars are disjoint + exhaustive.
• frequency = height of histogram bars.
• frequency density = area under histogram bar.

Question 31

Frequency polygon

Answer 31

• obtained by joining the top midpoint of each bar of the Histogram to each other/join top points of class midpoint + frequency density of each class.
• doesn’t represent basic data well.
• area under it is not proportional to frequencies.

Question 32

Frequency curve

Answer 32

• obtained by smoothing out frequency polygon.
• used to compare distribution of data sets.
• taken to represent the true distr. of popn from which sample is drawn.

Question 33

Class boundary

Answer 33

The exact value for each set of grouped data where one set of values ends & the other begins.