Statistics: Chapter 1 - Data Collection

Question 1

What is a Population

Answer 1

A population consists of all the items we are interested in.

(Note, there aren’t always people)

Question 2

What is a Sample

Answer 2

A sample is a subset of items chosen from a population.

Question 3

What is a Sampling Unit

Answer 3

Each individual item in the population that can be sampled is known as a sampling unit.

Question 4

What is a Sampling Frame

Answer 4

Often sampling units of a population are individually named or numbered to form a list called the sampling frame.

Question 5

Advantages and Disadvantages of a Census

Answer 5

Advantages:
- Should give completely accurate result.

Disadvantages:
- Time consuming and expensive
- Can not be used when testing involves destruction
- Large volume of data to process

Question 6

Advantages and Disadvantages of a Sample

Answer 6

Advantages:
- Less expensive
- Less time consuming
- Less data to process

Disadvantages:
- Data may not be accurate
- Sample mag not be large enough to represent small sun-groups of the population

Question 7

What is Random Sampling

Answer 7

Where each thing in your sample frame has an equal chance of being chosen.

Question 8

Method of how to do Simple Random Sampling

Answer 8

To carry out a simple random sample, size n, from a population size N, firstly you need a sampling frame.

Each item is assigned a different number from 1 to N. Use a random number generator to select ‘n’ unique numbers or ‘lottery sampling’ (names in a hat).

Choose the items corresponding to these numbers to form the sample.

Question 9

Advantages of Simple Random Sampling

Answer 9

• Bias free
• Easy and cheap to implement for small populations and samples
• Each sampling unit has a known equal chance of being selected

Question 10

Disadvantages of Simple Random Sampling

Answer 10

• Not suitable when population size is large
• Sample may not accurately reflect the population
• A sampling frame is needed

Question 11

Method of how to do Systematic Sampling

Answer 11

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

To carry out a systematic sample, size n, from a population, size N, you need a sampling frame.

Each item is assigned a different number from 1 to N. Starting at a random between 1 and k, take every k^th elements to form the sample k = pop size(N) / samp size (n)

Question 12

Advantages of Systematic Sampling

Answer 12

• Simple and quick to use
• Suitable for large samples and populations

Question 13

Disadvantages of Systematic Sampling

Answer 13

• Can introduce bias if sampling frame is small and not random as patterns can be picked up in the data
• A sampling frame is needed

Question 14

Method of how to do Stratified Sampling

Answer 14

Population divided into groups (strata) and a simple random sample carried out in each group.

To carry out a stratified sample, size n, from population size N, you need a sampling frame and distinct strata. The same proportion n/N is to be sampled from each strata.

Within each strata, each item is assigned a different number and a random number generator is used to select the number of unique numbers required.

Choose the items corresponding to these numbers to form the sample.

Question 15

Advantages of Stratified Sampling

Answer 15

• Sample accurately reflects population structure
• Guarantees proportional representation of groups within population

Question 16

Disadvantages of Stratified Sampling

Answer 16

• Sampling frame is needed and population must be clearly classified into distinct data
• Selection within each stratum suffers from same disadvantages as simple random sampling.

Question 17

Example Question:

There are 64 girls and 56 boys in a school. Explain briefly how you could take a random sample of 15 pupils using a random sample. (3 marks)

Answer 17

Using the school register as a sampling frame, assign each student a number between 1 to 120

Use a random number generator to select 15 unique numbers

Take the 15 students that correspond to those numbers as your sample

Question 18

Example Question:

A school has 15 classes and a sixth form. In each class there are 30 students. In the sixth form there are 150 students. There are equal numbers of boys and girls in the sixth form. The head teacher wishes to obtain the opinions if the students about school uniforms. Explain how the head teacher would take a stratified sample of size 40. (7 marks)

Answer 18

Population = (15x30) + 150 = 600

Sixth Form:

150/600 = 1/4
1/4 x 40 = 10 sixth formers
10/2 = 5
∴ 5 sixth form boys, 5 sixth form girls

Using the sixth form register as a sampling frame, assign the males a number from 1 to 75 and the females a number from 1 to 75. Then use a random number generator to select 5 unique males and 5 unique females to from part of the sample.

Rest of School/Classes:

30 students
30/15 = 2
∴ 2 students per class (1 male, 1 female)

Question 19

Example Question:

A telephone directory contains 50,000 names. A researcher wishes to select a systematic sample of 100 names from the directory. Explain in detail how the researcher should obtain a sample.

Answer 19

Using the telephone directory as a sampling frame, assign each name a number from 1 to 50,000.

50,000/100 = 500

Use a random number generator to select a number between 1 and 500, then starting with that name chosen every 500th name after that to form a sample of 100.