Statistics

Question 1

What is discrete data

Answer 1

non decimal/ non fractional number

for example number of children in a classroom (you can’t have decimal amount of children)

Question 2

What is continuous data?

Answer 2

includes decimals

E.G height, weight

Question 3

What is a measure of central tendancy?

Answer 3

where the center of our data falls

Question 4

What does it mean when data is skewed?

What is a positive skew and what is a negative skew? Draw them both

Answer 4

Data can be “skewed”, meaning it tends to have a long tail on one side or the other:

Question 5

When do you use mean as a measure of central tendency? When do you not use the mean as a measure of central tendency?

Answer 5

when your data distribution is continuous and symmetrical when it is quantitative and uses all pieces of its data

Not:

• when you have extreme values (outliers)
• when you have skewed data

Question 6

When do you use the median as a measure of central tendency

Answer 6

• when the data is quantitative
• used when there are extreme values as these do not affect the median

Question 7

When do you use the mode as a measure of central tendency?

Answer 7

used for nomial data (data that can be labelled or classified into mutually exclusive categories within a variable.

These categories cannot be ordered in a meaningful way.

For example, for the nominal variable of preferred mode of transportation, you may have the categories of car, bus, train, tram or bicycle)

Question 8

What are the advantages and disadvantages of box plots?

Answer 8

Pros:

• helps us to see the spread of data more easily
• plot is clear and easy to understand
• it uses range and median values
• it is easy to compare the stratified data

Cons:

• Original data is not clearly shown in the box plots
• mean and mode cannot be identified using the box plots
• it is easily misinterpreted
• if large outliers are present, the box plot is more likely to give an incorrect representation

Question 9

When is the regression line a valid model?

Answer 9

when the data shows linear correlation

stronger correlation = higher accuracy

When trying to estimate a DEPENDENT variable (y coord)

Question 10

What is a census? Name the pros and cons

Answer 10

When each member of a population is used

Pros:

• completely accurate

Cons:

• time-consuming
• expensive
• cannot be used when it destroys population
• hard to process large quantity if data

Question 11

What does a sampling frame mean?

Answer 11

the source material or device from which a sample is drawn

Question 12

What are the three METHODS of random sampling?

Give definitions

Answer 12

• simple random sampling= every sample size of n has an equal chance of being selected (uses sampling frame)
• Systematic sampling = the required elements are chosen at regular intervals from an ordered list
• Stratified sampling = population split into strata differences and a random sample taken from each

Question 13

What is the equation for the number sampled in strata?

Answer 13

number in strata/ number in population x overall sample size

Question 14

Why is random sampling useful?

Answer 14

it removes bias

Question 15

What are the pros and cons of simple random sampling?

Answer 15

Question 16

What are the pros and cons of systematic sampling

Answer 16

Question 17

What are the pros and cons of stratified sampling?

Answer 17

Question 18

What are the two types of NON-random sampling?

What are the definitions?

Answer 18

• Quota sampling = interviewer/ researcher slects the charcteristics of the whole population
• Opportunity (or convenience) sampling = taking the sample from people who are available at the time the study is carried out and who fit the criteria you are looking for.

Question 19

What are the pros and cons of Quota sampling?

Answer 19

Question 20

What are pros and cons of opportunity sampling?

Answer 20

Question 21

What are the types of data/variables

(data is interchangeable with variables)

Answer 21

• Quantitative data = data/variables associated with numerical observations
• Qualitative data= associated with non-numerical observations
• Continous variable = can take any value in a given range
• Discrete variable = only specific values in a given range (no decimals)

Question 22

What is meant by population?

Answer 22

a set of data that you can take a sample of

the whole set of items that are of interest

Question 23

When do you increase the lower and upper bound by 0.5

Answer 23

when the classes do not overlap

e.g. 10

Question 24

What is the equation for variance and standard deviation for raw data

Answer 24

Question 25

what does S_xx

What is variance in terms of S_xx

Answer 25

S_xx= (x_i- mean)²

Question 26

What is the equation for the mean and standard deviation for frequency tables?

Answer 26

Question 27

what does strata mean?

Answer 27

when the population is split into groups based on similar characteristics

Question 28

What does a statistic mean?

Answer 28

a random variable that is a function of a sample which contains no unknown quantities/parameters

Question 29

Inferential statistics - definition

Answer 29

methods of making decisions and predictions about a population based on a sample selected from the population.

Question 30

Sample- definition

Answer 30

A sample provides a set of data values of a random variable, drawn from all such possible values. A sample is a subset of the target population.

Question 31

parameter - defintion

Answer 31

a numerical summary of the population, examples are the population mean, and the population standard deviation

Population parameters are denoted using the Greek alphabet.

Question 32

proportional stratified sampling - defintion

Answer 32

The frequencies for each group in the sample are often proportional to the frequencies for each group in the population

Question 33

sampling distribution - definition

Answer 33

all possible values of a statistic together with their associated probabilities

Question 34

What is a residual

Answer 34

observed data - predicted

data above the line = positive residual

data below the line = negative residual

Question 35

What letter represents correlation coefficient ?

What is the correlation coefficient for positive, negative and no correlation

Answer 35

R

positive = 1

negative = -1

no = 0

Question 36

What is bivariate data?

What is it represented on?

Answer 36

data which has pairs of values for two variables

represented on scatter diagrams

Question 37

What does an explanatory variable and dependent variable mean?

Answer 37

explanatory variable = independent variable

dependent = response variable

Question 38

When can you use binomial distribution?

Answer 38

When there is:

• a fixed number of trials
• when there are two possible outcomes (success and failure)
• fixed probability of success
• when trials are independent of each other

Question 39

what is the definition of a significance level?

Answer 39

the probability of the data being in the critical region

Question 40

State the assumption involved with using class midpoints to calculate an estimate of
a mean from a grouped frequency table.

Answer 40

The spread of data values inside each class is evenly distributed around the
midpoint.

Question 41

When do you use normal distribustion? What are the assumptions with normal distribution ?

Answer 41

Used for large quantitative data

Symmetry around its mean. This means that the mean, median, and mode are all equal and located at the center of the distribution.

Bell-shaped Curve: The distribution has a bell-shaped curve, meaning that it has a single peak and tails that extend indefinitely in both directions.

Independence: The observations or measurements are assumed to be independent of each other. This assumption is important because the normal distribution assumes that the values do not influence each other’s probabilities.

Continuous Data: The normal distribution is appropriate for continuous data, where the values can take any real number. It may not be suitable for discrete or categorical data.

Question 42

When can you not use normal distribution?

Answer 42

Skewed Data: If your data is significantly skewed, meaning it is asymmetric with a long tail on one side, the normal distribution may not accurately represent the underlying distribution.

Outliers: When your data contains outliers, extreme values that are significantly different from the majority of the observations, the normal distribution may be sensitive to these outliers. Outliers can strongly influence the mean and standard deviation.

Categorical or Discrete Data: The normal distribution is suited for continuous data, where values can take any real number. However, if your data is categorical (e.g., yes/no, red/blue/green) or discrete (e.g., counts or whole numbers), the normal distribution is not applicable.

Small Sample Sizes: When you have a small sample size, the assumption of normality may be difficult to verify, and the distribution of your data may deviate from the normal distribution.

Non-Linear Relationships

Question 43

When can you not use binomial distributon

Answer 43

• multiple outcomes instead of just purely success or failure

Dependent Trials: The binomial distribution assumes that each trial is independent of the others

Continuous Data: The binomial distribution is designed for discrete data, where the outcomes are counted or represented as whole numbers.

large sample: Sample Size Too Large:
When the sample size is very large, the assumptions of the binomial distribution may not hold. One of the key assumptions of the binomial distribution is that the trials are independent and identically distributed. With an extremely large sample, it is possible for the independence assumption to be violated, as individual trials may become correlated. In such cases, alternative distributions like the normal distribution or the Poisson distribution might be more appropriate approximations.

When the sample size is small, it can lead to unstable estimates and imprecise results. The binomial distribution assumes a fixed number of independent trials, and with a small sample size, there may not be enough data to accurately estimate the underlying probability of success (p) for each trial.