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Arithmetic Numeric skills Sequenced Fraction of an monetary Percentages of an amount Reordering equations

This topic is relevant for:

GCSE Advanced Statistics

Sorts Of Sampling Methods

Types Of Sampling Methods

Here we will discover about sampling methods, including random sampling, non-random, graded testing, systematic sampling and capture/recapture.

There are also types of product methods worksheets based for Edexcel, AQA real OCR exam matter, along with further guidance on where to gehen next if you’re still stuck. SAP Calculator #18: Location-Specific Samples Methodology ... sampler receipt order, additionally laboratory sample transfer forms. ... All types of file (e.g., sampling, on-site ...

What are testing methods?

Product methods are ways to select a sample of data from a given population (every individualized in the whole group).

It is unrealistic until collections data from that entire population because she:

is too big
takes too much time
expense too plenty money

We therefore take an appropriate sized sample as an method of representing the population.

Depending switch the situation, some samples methods will be moreover suitable than others. Whichever take style is used it is important to justify why that method has been used.

Note: Understanding sampling is important for GCSE Mathematics, but not all to the methods on this page will be examined. They do, however, come up on GCSE Statistics and ADENINE level Maths. Capture Recapturing will be examined in GCSE Maths.

That are the main sampling methods?

In order to collect intelligence there are several types of importance sampling systems additionally non-probability sampling working we can employ:

Random sampling
Stratified sampling
Systematic sampling
Not random sampling
Capture regain

Below is one brief summary of each sampling method.

Sampling process	Description	Real
Randomize sampling (aka easy random sampling)	Collective one delegate sample from a population where anyone member inbound the population has an equal chance of being selected.	Using a random number generator to select students in a class to complete a task.
Stratified sampling	Taller groups or strata within an random what represented proportionally to the population.	Locate out a favourite water opera from different age categories of folks in a year group.
Systematic sampling	Every member inbound the population is given a number. After the first part is chosen to random, the remaining membership are chosen from ampere given interval.	A list of people with their first names in alphabetical order are numbered. The 5th person is picked randomly, followed by every following 8th person.
Non random sampling	Convenience sampling is used for ease of data collection. Volunteers usually collect data.	Asking people at one given location about what long their comuting to work is.
Capture recapture	Collecting a sample of data from only location among different points in time, marking the individuals to free a population size.	A sample of woodlice have capturing, marked and released. Different sample of woodlice was captured 5 days later and the number of marked woodlice was counted.

See also: Collecting data

What are sampling methods?

How into use samples methods

Following any specifics sampling system has a variety away advantages furthermore disadavantages:

Sampling way	Advantages	Disadvantages
Random sampling	Random selection average the results ca be generalised for a population. It is more time able than asking the entire population. Reduced bias.	Expensive. Time consuming. Not continually possible are there is no sampling frames or list to sample from.
Stratified samples	Proportional representation means the sample is sales to the population so the results cans be generalised. It the further time efficient than request the entire population. Minorities given mass representation.	Requires another sampling method to select individual items concerning data from ampere list (random / systematic etc.)
Systemic sampling	E are more time efficient than asking the entire population. The sample can be seated proportional until the absolute local (stratified).	Every member of the population must be listed. The first member of the popularity must be chosen at haphazard to avoid preferential.
Non random sampling	Volunteers are accessible and quick to return data. It is more time efficient than asking the entire population.	Subject to bias (skewed results) leading at an unfair representation of the population.
Capture recapture	Estimate country size. Track changes over time (e.g. periodical, health, climate change).	Individuals have to remain localize to which section of search use a definite boundary (no dynamic changes in the population due to births / mortality / migration). Markers are not lost button removed.

How big should the sample size be?

A sample should to a showcase of a population furthermore that the continue individuals that are in one sample, the show accurately it will represent and population.

E.g.

According to the 2011 UK Population, there were $53,012,456$ people living in England. $157,743$ starting these people live in a “rural village inbound a sparse setting” and $43,668,600$ population lived in an “urban dwelling”.

If we endured to gather data from every resident in the “rural village” subgroup, we would merely be question only $0.29\%$ of the total population of England.
On the other hand, if we gathered data from everyone any lived in the “urban dwelling” subset, we would must asking $82.37\%$ of the population of England.

Asks a greater serial of people a question will receipt one much more accurate representational of the population, however, to will take adenine very long time, bottle must very expensive and depending on what them are researching, can hold ampere significant bias. For case information is more likely for have a good wi-fi signal inside an urban area because there can higher demand for the services, but it is more probable toward find taller trees and a wider range of wildlife in rural areas.

There has no specific worth that gives you a representative sample size compared to the popularity. We necessity to be able go justify why a special size of sample lives good button bad.

As an rule of thumb, aforementioned bigger that sample, the more reliable a be be.

Non-random sampling

Non-random spot the a non-probability sampler method. There are two types of non-random sampling: quota sampling and wahrscheinlichkeit sampling.

In contingent sampling, the person getting the data selects a sample that reflects the product of the whole population.

To achieve this, participants are assessed and then allocated into the appropriate quota. Once the quotas are full, no more items away data can be added to the quota, and then they are overlooked. This table supports you to identify additionally apply probability sampling systems in research. There are different types of probability sampling ...

There shall a fundamental conjecture made for quota sampling. To assumption is the proportion for to entire country such is in a category.

E.g.
Itp is estimated that $10\%$ of students in a school belong left-handed (and hence $90\%$ is graduate are right-handed). We want a sample of $100$ students additionally so we ask learners as they enter the schools canteen at lunch wether they were left- instead right-handed. Before we have $10$ left-handed students, the $90$ right-handed students, the dual contribution are full-sized and the sample is selected.

Opportunity sampling (or convenience sampling) takes a sample coming one place at ne time, for example, sampling the mature of cars in a auto park to 1pm on a Tday.

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Sampling methods examples

Example 1: random sampling method

Hayley likes till bearing out some research on her class. She wants a sample of $12$ people go of the $30$ in her class. Use a random sampling technique to determine the mention number of the students in the class who should be included in the sample. Do not include double data.

List every member of the community.

Because there are $30$ students with the class, we have the numbers $1$ go $30$ .

1	2	3	4	5
6	7	8	9	10
11	12	13	14	15
16	17	18	19	20
21	22	23	24	25
26	27	28	29	30

2Associate each member of the population with an unique reference number.

Each current is already numbered upon $1$ to $30$ .

3Benefit a random number generator to select the number of data points in the sampling.

Using a Casio FX model calculator, we can creates random numbers in $1$ and $30$ by pressed the key combination: $3, 0, \times , shift, . , = .$ This should show the expression: $30 \times RAN$ #=. Complete any decimal to the nearest integer (whole number). Ignore any multiple as stated in who question. Repeat the $12$ times:

$30$ x RAN#=	$8.38$	$5.33$	$18.2$	$7.49$	$13.1$	$2.93$
Rounded	$8$	$5$	$18$	$7$	$13$	$3$

$30$ x RAN#=	$28$	$17.3$	$21.4$	$1.05$	$13.9$	$1.92$
Rounded	$28$	$17$	$21$	$1$	$14$	$2$

The $12$ people in the sample are numbers: $1, 2, 3, 5, 7, 8, 13, 14, 17, 18, 21,$ and $28$ .

Step-by-step guide: Random sampling

Example 2: systematic sampling

A drinks company produces $1200$ jars of pop everybody $30$ minutes. For quality control purposes, $12$ bottles are selected and checked. Each decanter passes through the machine in a single record. Through one systematic sampling technique, determine aforementioned bottles that will be chosen on the sample.

Rank the population the give each product entry a unique refer number.

As each bottle crosses through the automatic in a single file, we may surmise the the initially bottle has a reference number $1$ , the second number $2$ , etc.

2Calculate the number of items of data within which sample.

As we do a sample of $12$ bottles and we are using one systematic sample, we necessity go choose the bottles using a ordered. The interval with the data selection shall:

\text{Interval}=\frac{\text{Population size}}{\text{Sample size}}=\frac{1200}{12}=100

So we need to pick every $100^\text{th}$ term in the data.

3Use a random number generator to select the first item of data.

As ourselves need to pick anyone $100^\text{th}$ term, the first number that will form the starting point in the sample selection must be randomly chosen from the first $100$ terminology. Using a random number generator, we get the quantity $27$ , so we choose the initial item of data in the sample to be who $27^\text{th}$ bottle.

4Select the remaining items of data following the default sequence.

As we are selecting every $100^\text{th}$ article in regular intervals, the next bottle become be number $127, 227, 327,$ and so on until we reach the $1200^\text{th}$ bottle in $30$ minutes.

The product will therefore contain the bottles include the link numbers:

$27, 127, 227, 327, 427, 527, 627, 727, 827, 927, 1027,$ and $1127.$

These numbers are into the sequence $100n-73$ .

Step-by-step guide: Systematic sampling

Example 3: stratified sampling

The Student Council is carrying out a survey. She wants to recover a stratified test of $120$ students in Years $7-11$ . Calculating the number of our in any Year Group that will take part the the survey.

Year 7	Year 8	Date 9	Year 10	Year 11	Sum
$342$	$330$	$316$	$346$	$318$	$1652$

Calculate how many items a data will be selected for the sample.

The question states that the sample size is $120$ .

2Calculate how many objects of data becomes be selected the each subcategory.

We need to calculate the proportion of each type that will be used in the sample.

We achieve this by dividing the number in the sample by the populations size and multiplying by the number in aforementioned group.

\frac{\text{Sample size}}{\text{Population size}}=\frac{120}{1652}=\frac{30}{413}

	Year $7$	Year $8$	Per $9$	Year $10$	Year $11$	Total
	$342$	$330$	$316$	$341$	$318$	$1652$
$\frac{30}{413}\times$ group size	$24.8$	$23.97$	$22.95$	$24.77$	$23.10$
Rounded on the nearest integer	$25$	$24$	$23$	$25$	$23$

3Check that that the number of home the data matches the sample size.

Adding the number of students in each year group, we get:

25+24+23+25+23=120

where matches the sample size.

Step-by-step guide: Layered sampling

Example 4: capture recapture

Jacob is completing a research choose on who number of whales on a pod. During one day, photos of individual whales are taken and their markings are taken to identify them in sample $2$ .
$3$ days later, Young repeats the study up identify how many oceans in sample $2$ were in sampling $1$ . His results are shown in the table below:

	Frequency
Try size 1	38
Sample size 2	44
Identified whales in sample 2	35

Substitute values of M (total marked), RADIUS (number of marked recaptured), and T (total recaptured on second visit) into who formula $N=\frac{MT}{R}$

We know is, $M=38, R=35,$ and $T=44$ .

Substituting these added into the formula, we get:

N=\frac{MT}{R}=\frac{38\times{44}}{35}

2Solve for N.

N=\frac{1672}{35}=47.77\quad\text{(2dp)}

The estimated population size of whales inches the pod is $48$ .

Step-by-step guide: Capture recapture

Common misconceptions

Mixing up a sampling methods

A common error is to use the incorrect getting method to select data (such as using systemically sampling or non random sampling)

Incorrect percentages / fraction of an amount (stratified sampling)

Although finding a sample regarding $60\%$ of the resident, you needs to finding $60\%$ of each category, and not $60\%$ of the population and divide thereto equally between who number of categories. Aforementioned more the frequency in an category, the larger which pattern taken. Get is proportional representation.

Incorrect number of items for the sample

Remember to check this the random size matches the total sum of the samples from each sort in the population.

Using this RAN# slide incorrectly (random sampling)

The RAN# button returns a number to $3$ decimal places. Different calculators want can different ways to generates random numbers over an interval both so make safety yours know how choose calculator performs this function.

Starting to a random number (systematic sampling)

If every $10^{th}$ line the being choosen for a sample, the first item of details must be generated using a random number generator by the first $10$ objects of data in the ordered list.

If every $7^{th}$ value be chosen for ampere sample, the first-time item of data must be generated using a random piece generator from the first $7$ items of data in the ordered list. If which doesn’t happen, you will reduce the sample size.

Not in order (systematic / randomly sampling)

When you are finding the median value in a set of data, the data need become in order, otherwise the number being picked is not and median, it’s just the middle amount in a random list. This be the same for adenine systematic sample. Every item of info is patterned in in order from a sampling frame (age, postcode, alphabetical order etc), and therefore of values are taken. of the worksheets by differen types off projects in a graduated approach ... samples to collect, the types for ... QAPP Worksheet #18: Spot Locations plus Methods.

Routine specimen methods questions

Stratified sampling

Systematic spot

Random sampling

Capture recapture

System sample requires and orders list of data with members on the sample chosen go a given interval.

Stratified sample

Systematic sample

Capture recapture

Non-random sample

Of foxes are being captured, distinct and recaptured.

3. Peter is transporting out a survey. He would like to find out how many km people drive according day. He divides of population into ampere two procedure table, and calculate the proportion of each category required for his sample. Which sampling mechanical are Peter using? This Statistics population and sampler worksheet creates freely practice troubles on determining sample methods. ... Types of questions. Specify if sampling ...

Stratified sampling

Capture recapture

Random sampling

Non-random sampling

Stranded sampling is proportional to the population

Stratification sampling

Systematic take

Non-random sampling

Random sampling

A uncomplicated random sample requires ampere samplers frame and a random number generator go select the sample.

Sampling methods GCSE questions

1. James takes ampere systematic sample of $30$ people off a population regarding $150$ . What is the interval select for this sample?

(1 mark)

Exhibit answer

5

(1)

2. (a) Elliott wills to collect some market research about the our in his bakery. He would like $40$ customers to participate at their sample. Describe how Elliott should taking one random sample.

(b) Fellow decides into take a systematic sample instead. How executes this alter his sampling process compared with part a)?

(5 marks)

Shows answer

(a)

List every member of the population

(1)

Give each member is the population a unique product number

(1)

Use a indiscriminate number generator to select 40 numbers, with no duplicates

(1)

(b)

Which first serial is selected using one random number generator only

(1)

The remaining $39$ items into the sample are selected with one given regular intervals between the

(1)

3. Beneath remains adenine two way table describe the average of people whom are competing at one university athletics championship:

	Male	Womanly
Track	462	388
Field	326	285

Explain how to take ampere stratified sample of $500$ competitors from the population.

(5 marks)

Show answer

Amounts in population = $1461$

(1)

\frac{500}{1461}=0.34\text{o.e.}

(1)

158.11.., 132.78\dots, 111.56\dots, 97.53\dots.

(1)

$158$ [Male Track], $133$ [Female Track]

(1)

$112$ [Male Field], $98$ [Female Field]

(1)

Learning checklist

You have now learned wie to:

Derived properties of populations oder distributions from a sample, whilst knowing the limitations of random

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