Chapter 1

Question 1

What is a population in statistics?

Answer 1

A population is the whole set of items that are of interest.

Question 2

What is a census?

Answer 2

A census observes or measures every member of a population.

Question 3

What is a sample?

Answer 3

A sample is a selection of observations taken from a subset of the population which is used to find out information about the population as a whole.

Question 4

What is a sampling unit?

Answer 4

Individual units of a population are known as sampling units.

Question 5

What is a sampling frame?

Answer 5

Sampling units of a population are individually named or numbered to form a sampling frame.

Question 6

What is a simple random sample?

Answer 6

A simple random sample of size
𝑛
n is one where every sample of size
𝑛
n has an equal chance of being selected.

Question 7

What is systematic sampling?

Answer 7

In systematic sampling, the required elements are chosen at regular intervals from an ordered list.

Question 8

What is stratified sampling?

Answer 8

In stratified sampling, the population is divided into mutually exclusive strata (e.g., males and females), and a random sample is taken from each.

Question 9

What is quota sampling?

Answer 9

In quota sampling, an interviewer or researcher selects a sample that reflects the characteristics of the whole population.

Question 10

What is opportunity sampling?

Answer 10

Opportunity sampling consists of 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 11

What are quantitative variables?

Answer 11

Variables or data associated with numerical observations are called quantitative variables or quantitative data.

Question 12

What are qualitative variables?

Answer 12

Variables or data associated with non-numerical observations are called qualitative variables or qualitative data.

Question 13

What is a continuous variable?

Answer 13

A variable that can take any value in a given range is a continuous variable. (e.g., temperature, windspeed).

Question 14

What is a discrete variable?

Answer 14

A variable that can take only specific values in a given range is a discrete variable. (e.g., number of days with rain).

Question 15

What is a class in grouped data?

Answer 15

When data is presented in a grouped frequency table, the specific data values are not shown. The groups are more commonly known as classes.

Question 16

What are class boundaries?

Answer 16

Class boundaries tell you the maximum and minimum values that belong in each class

Question 17

What is the midpoint of a class?

Answer 17

The midpoint is the average of the class boundaries.

Question 18

What data is included in the large data set?

Answer 18

The large data set contains data for a number of different variables at eight weather stations.

Question 19

What variables are recorded in the large data set?

Answer 19

Daily mean temperature (°C)
Daily total rainfall (mm)
Daily total sunshine (hours)
Daily mean wind direction and windspeed (knots)
Daily maximum gust (knots)
Daily maximum relative humidity (%)
Daily mean cloud cover (oktas)
Daily mean visibility (Dm)
Daily mean pressure (hPa)

Question 20

What is recorded as ‘tr’ in daily total rainfall?

Answer 20

‘tr’ (trace) means an amount less than 0.05 mm.

Question 21

What is the Beaufort scale used for in the large data set?

Answer 21

The Beaufort scale is used to categorise wind speed.
Calm (0) = Less than 1 knot
Light (1–3) = 1–10 knots
Moderate (4) = 11–16 knots
Fresh (5) = 17–21 knots

Question 22

What is a knot (kn)?

Answer 22

1 knot = 1.15 mph.

Question 23

What are oktas?

Answer 23

Oktas measure cloud cover in eighths of the sky covered by clouds.

Question 24

What is daily mean pressure measured in?

Answer 24

Daily mean pressure is measured in hectopascals (hPa).

Question 25

Why is familiarity with the large data set important?

Answer 25

You may need to recall trends from within the large data set or identify a location based on given data.

Question 26

Give one advantage and one disadvantage of a systematic sample

Answer 26

✅ Advantage: Simple & quick for large datasets. ❌ Disadvantage: Can introduce bias if data is arranged in a patterned order.

Question 27

Give one advantage and one disadvantage of a quota sample

Answer 27

✅ Advantage: Ensures a representative selection based on characteristics. ❌ Disadvantage: Can introduce interviewer bias.

Question 28

Why might a systematic sample be used for analysis?

Answer 28

It ensures even coverage across the dataset (e.g., selecting every 5th data entry).

Question 29

Why is it important to understand limitations of the large data set?

Answer 29

Some values may be missing → Not all data is available. Not representative of all weather conditions → Only covers certain locations & time periods. Rounded data → Some values (e.g., sunshine, temperature) may be approximated.

Question 30

Give one advantage and one disadvantage of opportunity sampling.

Answer 30

✅ Advantage: Easy & inexpensive to carry out. ❌ Disadvantage: Unlikely to be representative of the population

Question 31

Give one advantage and one disadvantage of quota sampling

Answer 31

✅ Advantage: No sampling frame needed, quick and cost-effective. ❌ Disadvantage: Can introduce bias if the interviewer makes subjective decisions.

Question 32

How does opportunity sampling work?

Answer 32

A sample is taken from people available at the time (e.g., the first 20 people outside a supermarket).

Question 33

What formula is used for stratified sampling?

Answer 33

Number sampled in stratum= Number in population / Number in stratum ​ ×Overall sample size

Question 34

How does stratified sampling work?

Answer 34

The population is divided into mutually exclusive groups (strata), and a random sample is taken from each group.

Question 35

What are the advantages and disadvantages of simple random sampling?

Answer 35

✅ Advantages: Free of bias Each sample unit has an equal chance of selection ❌ Disadvantages: Not suitable for large populations Time-consuming if sample size is large

Question 36

What are the two ways to select numbers for a simple random sample?

Answer 36

1️⃣ Random number generator (calculator, computer, or number table). 2️⃣ Lottery method (write names on tickets and draw from a hat).

Question 37

How does simple random sampling work?

Answer 37

Every sample of size n has an equal chance of selection

Question 38

What are the three types of random sampling?

Answer 38

1️⃣ Simple Random Sampling 2️⃣ Systematic Sampling 3️⃣ Stratified Sampling

Question 39

Give one advantage and one disadvantage of using a sample.

Answer 39

✅ Advantage: Quicker & cheaper than a census. ❌ Disadvantage: Data may not be as accurate, especially if the sample is too small.

Question 40

Give one advantage and one disadvantage of a census.

Answer 40

✅ Advantage: Should give a completely accurate result. ❌ Disadvantage: Time-consuming and expensive, especially for large populations.