Systematic sampling - small-scale

Dann Mallet mathematics
26 Sept 201704:17
EducationalLearning
32 Likes 10 Comments

TLDRThis video tutorial demonstrates the process of systematic sampling to select six plastic office chair mats from a production run of 500. The method involves calculating a regular interval by dividing the total number of items (500) by the sample size (6), resulting in an interval of approximately 83. Starting from the 407th chair mat, the video guides viewers through the selection process, including looping back to the beginning of the list when exceeding the population size. The final systematic sample consists of chair mats numbered 407, 490, 73, 156, 239, and 322, effectively illustrating the systematic sampling technique.

Takeaways
  • 📚 The video discusses Question 2 from Exercises 4.2 in a math textbook, focusing on systematic sampling.
  • 🔍 The task is to use systematic sampling to select six plastic office chair mats from a production run of 500.
  • 📐 Systematic sampling involves choosing items at regular intervals from a larger population.
  • 🎯 The starting point for the sampling is given as the 407th chair mat.
  • 🔢 To determine the sampling interval, divide the total population (500 mats) by the sample size (6 mats), which equals approximately 83.
  • 📈 The first sample is taken at the starting point (407), and subsequent samples are taken every 83rd item.
  • 🔄 When the calculated interval exceeds the population size, the process loops back to the beginning of the list.
  • 📝 The selected chair mats using systematic sampling are numbers 407, 490, 73, 156, 239, and 322.
  • 📉 The process ensures an equal probability of selection for each item in the population, maintaining the representativeness of the sample.
  • 📋 The video provides a step-by-step guide on how to perform systematic sampling, emphasizing the importance of regular intervals and looping back when necessary.
  • 📘 The final takeaway is the practical application of systematic sampling in a real-world scenario, such as quality control in a production line.
Q & A

  • What is the topic of the video?

    -The video discusses the process of using systematic sampling to select six plastic office chair mats from a production run of 500.

  • What is systematic sampling?

    -Systematic sampling is a method of selecting a sample from a population by choosing items at regular intervals.

  • How many chair mats are in the total production run mentioned in the video?

    -There are 500 plastic office chair mats in the total production run.

  • What is the sample size the video asks to select using systematic sampling?

    -The video asks to select a sample size of 6 chair mats.

  • What is the starting point for the systematic sampling as mentioned in the video?

    -The starting point for the systematic sampling is chair mat number 407.

  • How is the interval for systematic sampling calculated in the video?

    -The interval is calculated by dividing the total number of items in the population (500) by the sample size (6), which gives an approximate interval of 83.

  • What happens when the calculated interval exceeds the population size?

    -When the calculated interval exceeds the population size, the process loops back to the start of the list.

  • What is the first chair mat selected after applying the interval of 83?

    -The first chair mat selected after applying the interval of 83 is number 490.

  • How does the video handle the situation when the sum of the starting point and interval exceeds the total population?

    -The video suggests looping back to the start of the list and continuing the selection process from there.

  • What are the final selected chair mat numbers using systematic sampling as per the video?

    -The final selected chair mat numbers are 407, 490, 73, 156, 239, and 322.

  • What is the purpose of using systematic sampling in this context?

    -The purpose of using systematic sampling in this context is to ensure a representative and evenly distributed selection of chair mats from the production run.

Outlines
00:00
📐 Introduction to Systematic Sampling for Office Chair Mats

This paragraph introduces the task of using systematic sampling to select six plastic office chair mats from a production run of 500. The starting point is given as the 407th chair mat. The concept of systematic sampling is explained, which involves selecting items at regular intervals from a population. The population in this case is the 500 office chair mats. The goal is to determine the interval for selecting six mats from this population.

🔍 Calculating the Sampling Interval for Systematic Sampling

The paragraph explains the process of calculating the interval for systematic sampling. It is determined by dividing the total number of items in the population (500 office chair mats) by the number of items to be sampled (6). The calculation results in an interval of approximately 83, meaning every 83rd chair mat should be selected starting from the 407th mat.

🔄 Applying the Interval and Dealing with the Loopback

The paragraph details the application of the calculated interval in the systematic sampling process. It starts with the 407th chair mat and adds the interval of 83 to find subsequent samples. However, when the addition exceeds the population size (500), a loopback to the start of the list is necessary. This ensures that the total number of samples does not exceed the population size.

📝 Finalizing the Systematic Sample Selection

The final paragraph concludes the systematic sampling process by listing the selected chair mat numbers: 407, 490, 73, 156, 239, and 322. It confirms that six chair mats have been chosen as required, and it reiterates the systematic sampling method used: starting at the 407th mat and moving forward by the interval of 83, with adjustments for looping back when exceeding the population size.

Mindmap
Keywords
💡Systematic Sampling
Systematic sampling is a method of selecting a sample from a population by choosing elements at regular intervals. In the context of the video, it is used to select six plastic office chair mats from a production run of 500. The script explains that the interval for selection is determined by dividing the total population (500 mats) by the sample size (6 mats), resulting in an interval of approximately 83. This method is central to the video's theme, as it demonstrates how to apply systematic sampling in a practical scenario.
💡Population
In statistics, the population refers to the entire set of items or individuals that are the subject of a study. In the video, the population is the 500 office chair mats from which a sample is to be drawn. The concept of population is fundamental to understanding the video's content because it sets the stage for the sampling process and helps define the scope of the systematic sampling method.
💡Sample
A sample is a subset of a population that is selected for analysis. The video's main theme revolves around choosing a sample of six chair mats using systematic sampling. The script illustrates this by calculating the interval for selection and then applying it to the starting point (chair mat 407) to identify the selected samples.
💡Interval
In the context of systematic sampling, the interval is the regular distance between each selected sample. The script defines the interval as the total number of items in the population (500) divided by the number of items to be sampled (6), which equals approximately 83. This interval is crucial for the systematic sampling process and is used to determine the specific chair mats that will be selected.
💡Starting Point
The starting point in systematic sampling is the initial element from which the selection process begins. In the video, the starting point is given as chair mat 407. This concept is important because it sets the first element in the sequence of samples that will be chosen according to the calculated interval.
💡Plastic Office Chair Mats
Plastic office chair mats are the specific items being sampled in the video. They represent the population from which the sample is drawn. The script uses these mats as an example to demonstrate the process of systematic sampling, making them a key element in understanding the practical application of the method.
💡Production Run
A production run refers to a specific batch or series of items that are manufactured. In the video, the production run of 500 refers to the total number of plastic office chair mats that have been produced and are available for sampling. This term helps to contextualize the population from which the sample is being drawn.
💡Calculation
Calculation is the process of computing or determining a value or result. In the video, calculation is used to determine the interval for systematic sampling by dividing the total number of chair mats (500) by the sample size (6). This step is essential for understanding how to apply systematic sampling correctly.
💡Looping Back
Looping back refers to the process of returning to the beginning of a sequence when the calculated interval exceeds the size of the population. In the script, when the addition of the interval (83) to a selected mat number exceeds 500, the process loops back to the start of the sequence. This concept is important for understanding how to handle situations where the interval extends beyond the population size.
💡Selection
Selection in the context of the video refers to the act of choosing specific items from the population based on the systematic sampling method. The script details the selection of chair mats number 407, 490, 73, 156, 239, and 322, illustrating how the systematic sampling process results in a specific set of samples.
Highlights

The video discusses systematic sampling to select six plastic office chair mats from a production run of 500.

Systematic sampling involves choosing a sample at regular intervals from a list of items.

The total population for sampling consists of 500 office chair mats.

The interval for systematic sampling is determined by dividing the total population by the sample size.

The interval calculation results in approximately 83, meaning every 83rd mat is selected.

The starting point for selection is the 407th chair mat as per the question's instructions.

The selection process involves adding the interval of 83 to the starting point repeatedly.

When the selection exceeds the population size, the process loops back to the start.

The first selected chair mat after starting at 407 is 490 (407 + 83).

The second selection, after looping back, is the 73rd chair mat.

The third selection is the 156th chair mat, calculated by adding the interval to the previous selection.

The fourth selection is the 239th chair mat, following the systematic sampling method.

The fifth selection is the 322nd chair mat, continuing the systematic sampling process.

A total of six chair mats are selected using systematic sampling.

The selected chair mats are 407, 490, 73, 156, 239, and 322.

The video demonstrates the practical application of systematic sampling in a real-world scenario.

Systematic sampling is highlighted as an effective method for selecting a representative sample.

Transcripts

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Systematic SamplingMathematicsEducationalOffice ChairsProduction RunSampling MethodStatistical AnalysisData CollectionSampling IntervalPopulation Size