Introduction To Statistics

Question 1

What is statistics?

Answer 1

Statistics is the science of collecting, organising, analysing, and interpreting data.

Question 2

What can statistics be divided into?

Answer 2

1. Descriptive or deductive statistics
2. Inferential statistics.

Question 3

What is a Bernoulli trial?

Answer 3

It is a random experiment that results in only two possible outcomes: success or failure.

Question 4

What is a binomial experiment?

Answer 4

It is an experiment achieved by repeating independent Bernoulli trials n-times while keeping track of the total number of successes.

Question 5

What is the binomial formula?

Answer 5

For n-trials, the probability that k number of successes are gotten is given by,
P(k) = nCk • P^k(1 - P)^{n - k}
k is also the desired number of successes.

Question 6

What is the mean of a binomial distribution?

Answer 6

u = np,
Where n is the number of trials, p is the probability of a success.

Question 7

What is the formula for variance of a binomial distribution?

Answer 7

Variance = np(1 - p)

Question 8

What is Descriptive or Deductive statistics?

Answer 8

It is a branch of statistics involved solely in the collection and organising of data, without making inferences based on it.

Question 9

What is inferential statistics?

Answer 9

It is a branch of statistics which involves making predictions or inferences from data collected, usually generalising from sample data to population under study.

Question 10

What are the main sources of data?

Answer 10

Primary data: data collected first hand, usually through surveys and experiments.

Secondary data: data that had been collected by a third party; an organisation or individual that is different from the one making use of the data.

Question 11

What are the advantages of primary data?

Answer 11

1. Up to date
2. Specific to the needs of the party making use of it.

Question 12

What are the disadvantages of primary data?

Answer 12

1. Time consuming.
2. Can be very costly.

Question 13

What are the advantages of secondary data?

Answer 13

1. Easy to obtain
2. Not very costly
3. Not as time consuming.
4. Can consist of a huge bank of data collected over a long period of time.

Question 14

What are the disadvantages of secondary data?

Answer 14

1. Can be outdated
2. May not be specific to one’s needs.
3. May be biased in favour of the party who collected the data.
4. May not be as accurate as one would prefer.

Question 15

Based on the scales of measurement, how can data be classified?

Answer 15

NOIR
1. Nominal Scale
2. Ordinal Scale
3. Interval Scale
4. Ratio Scale

Question 16

Describe norminal scale.

Answer 16

It is a type of scale where the data collected is mutually exclusive with no order. Examples: male and female, married and single, etc.

Question 17

Describe the ordinal scale.

Answer 17

Data defined by (collected using) this scale can be ranked although there are no precise differences between ranks. E.g. quality grades like A, B, C; Upper, middle, and lower class citizens.

Question 18

Describe the interval scale.

Answer 18

Data collected using this scale can be ranked and have precise distinctions between ranks, but there is no true zero.
Example are the Celsius and Fahrenheit scales, where the difference between each unit in the scale is uniform and precise (one) but 0°C or 0°F is not the absence of thermal temperature. (0°F is still 273k)

True zero is the absolute absence of a quality being measured.

Question 19

Describe ratio scale.

Answer 19

Ratio scale can be ranked, has a precise distinction between ranks, and has a true zero. Examples include height, weight, volume, and the Kelvin scale.

Question 20

What is the variance of an independent variable X?

Answer 20

Variable(X) = E(X²) - (E(X))²

Question 21

What does Var(aX + b) or Var(aX - b) imply?

Answer 21

Var(aX + b) = a² × Var(X)