Section A.1: Introduction to Statistics

Question 1

What is data?

Answer 1

Data are measurements or observations collected as a source of information

Question 2

What is statistics?
(A, I, P, O)

Answer 2

Statistic is a branch of mathematics which deals with the
- Analysis
- Interpretation
- Presentation
- Organisation
of data.

Question 3

What are the two types of statistical analysis?

Answer 3

Descriptive analysis, and inferential analysis

Question 4

Descriptive statistics

Answer 4

Descriptive statistics refers to the statistical measures used to summarise and describe the basic properties of data, it is used in univariate, bivariate, and multivariate analysis.

Question 5

Types of statistical measures in descriptive statistics (2)

Answer 5

Measures of Central Tendency
Measures of Dispersion/Variability

Question 6

Inferential statistics

Answer 6

Inferential statistics refers to the processes that make inferences about a population based on a representative sample of the population.

Question 7

Define statistical analysis

Answer 7

Statistical analysis refers to the analysis of data in order to gather insights, and discover underlying patterns and trends.

Question 8

Define: Population Distribution

Answer 8

Population Distribution refers to the spread of a characteristic or variable across an entire population

Question 9

What is meant by sample?

Answer 9

Sample refers to a subset of a population that is selected to represent the entire population

Question 10

Categorical Variable

Answer 10

A categorical variable is a type of variable which is character or feature-based. Any variable which is not numerical. It is qualitative (characterised by qualities or features) and descriptive in nature.

Question 11

Categorical variable data types (3)

Answer 11

Nominal - which has no order or ranking
Binary data - Data which has exactly two possible values (eg. True, False)
Ordinal - has a natural order or ranking

Question 12

Nominal data does not have a natural order or ranking (T/F)

Answer 12

True, it does not have a natural order or ranking.
Eg. Gender, eye colour.

Question 13

Ordinal data

Answer 13

Ordinal data is data that has a natural order or ranking.
Eg. Education level, size (small, medium, large)

Question 14

Binary Data

Answer 14

A type of nominal data which has exactly two possible values
Eg. A or B, Yes or No.

Question 15

Numerical variable - data types (2)

Answer 15

Discrete and Continuous

Question 16

Discrete data

Answer 16

Data that can only take on certain values, usually whole numbers, NOT like continuous data.
Eg. Number of siblings

Question 17

Continuous data

Answer 17

Continuous data is data that can take on ANY value in a range, NOT like discrete data.
Eg. Height, temperature

Question 18

Data Dimension

Answer 18

Data dimension refers to the number of variables or features in a dataset.

“A dataset can have one, two, or more dimensions depending on the number of variables being measured.”

Question 19

Data Dimension types (3)

Answer 19

Univariate or one-dimensional: One variable (age)
Bivariate or two-dimensional: Two variables (age vs. height)
Multivariate (three-dimensional or more): 3 or more variables (Age vs. height vs. weight)

Question 20

Variable

Answer 20

A variable is a characteristic or attribute that can take on different values for different observations

Question 21

Independent variable

Answer 21

An independent variable is a variable that is manipulated or controlled by the researcher in a study to measure its effect on the dependent variable/s. It is plotted on the x-axis.

Question 22

Dependent variable

Answer 22

A dependent variable is a variable which response is being measured or predicted in a study. Plotted on the y-axis.

Question 23

What are bar graphs used for?

Answer 23

Bar graphs are used to visualise and compare groups of categorical data, the frequency of observations, distribution of observations, and/or compare magnitudes among them.

Question 24

What are bar graphs not used for? (2)

Answer 24

Numerical data (that is a histogram), and continuous or categories that are not independent of each other.

Question 25

What is a scatter plot used/useful for?

Answer 25

Scatter plots are useful for visualising and comparing patterns, trends, and relationships in numerical continuous data, and identifying outliers.

Question 26

What is a line graph useful for?

Answer 26

Line graphs are useful for visualising and comparing patterns, trends, and relationships, among continuous numerical variables, over time.

Question 27

What is a histogram used for?

Answer 27

A histogram is used to visualise grouped continuous data to compare the ranges of values and see the shape of distribution among those groups.

Question 28

What is a pie chart used for?

Answer 28

A pie chart is used to visualise categorical univariate data. They show the proportion of observations in different categories/groups in relation to a whole.

Question 29

Data Exploration

Answer 29

Data exploration is the initial analysis of data to understand its basic properties, patterns, and relationships

Question 30

Techniques for visualising univariate categorical data (3)

Answer 30

Frequency table, Bar chart, Pie chart

Question 31

Predictive modelling

Answer 31

Predictive modelling refers to tehniques and processes used to generate a predictive model which can predict a value of a dependent variable when only the predictor/independent variable/s value is known.

Question 32

Standard deviation calculation steps

Answer 32

1. Find the variance of all values in the data set
2. Square all of these values
3. Get the sum of those values
4. Divide by number of values in the data set
5. Get the square root of that value

Question 33

Techniques for visualising and analysing numerical univariate data (3)

Answer 33

Descriptive statistics, box plots, histograms