Ch.1 Data Collection PDF

Data Collection Cheat Sheet Edexcel Stats/Mech Year 1 Population and sample...

Data Collection Cheat Sheet Edexcel Stats/Mech Year 1 Population and sample Systematic sampling Non-random sampling In statistics, population is the whole set of items that are of interest. Information The required elements are chosen at regular intervals from an ordered list. There are two types of non-random sampling that you need to know: obtained from a population is known as raw data. A census measures or observes every Quota sampling member of a population. A sample is a selection of observations taken from a subset of Example 2: A sample of size 20 is required from a population of 100. An interviewer or researcher selects a sample that reflects the population and used to find out more information about the population as a whole. characteristics of the whole population. 100 ÷ 20 = 5 so every fifth person is chosen. Advantages Disadvantages Advantages Disadvantages The first person is chosen at random. Allows a small sample to Non-random sampling can Census Results should be completely Time consuming and expensive If the first person chosen is 2, the remaining samples will be 7, 12, 17 etc. still be representative of introduce bias accurate Cannot be used when testing the population Population must be divided Advantages Disadvantages destroys process No sampling frame into groups, which can be Hard to process large quantity of Simple and quick to use A sampling frame is needed required costly or inaccurate data Suitable for large samples Bias introduced if sampling frame is not Quick, easy and Increasing scope of study Sample Less time consuming and Data may not be as accurate and large populations random inexpensive increases number of cheaper Sample may not be large enough Easy comparison groups, which adds time Fewer people have to respond to give information about small between different and expenses Less data needs to be processed subgroups of the population Stratified sampling groups within a Non-responses not The population is divided into mutually exclusive strata and a random sample is population recorded Individual units of a population are known as sampling units. Sampling units are named taken from each. number in stratum and numbered to form a list called a sampling frame. Number sampled in a stratum= x overall sample size number in population Opportunity sampling or convenience sampling Random sampling Sample is taken from people who are available at the time of Example 3: A factory manager wants to find out about what his workers think Each member of the population has an equal chance of being selected. The sample study and who fits the criteria you are looking for. about the factory canteen facilities. He decides to give a questionnaire should be representative of the population and bias should be removed. There are 3 Advantages Disadvantages to a sample of 80 workers. It is thought that different age groups will types of random sampling. have different opinions. Easy and inexpensive Unlikely to provide a representative result Simple random sampling There are 75 workers between ages 18 and 32, 140 workers between ages 33 Highly dependent on A simple random sample of size 𝑛 is one where every sample of size 𝑛 has an equal and 47, and 85 workers between ages 48 and 62. individual researcher chance of being selected. Explain how he can use stratified sampling to select the sample. Types of data Example 1: The 100 members of a yacht club are listed alphabetically in the Variables or data associated with numerical observations are called club’s membership book. The committee wants to select a sample 1. Total number of workers: 75 + 140 + 85 = 300 quantitative variables or quantitative data. of 12 members to fill in a questionnaire. Explain how a simple 2. Finding the number of workers needed from each age group: random sample can be taken using: 75 Variables associated with non-numerical observations are qualitative 18-32: × 80 = 20 workers 300 140 1 variables or qualitative data. A) Calculator or random number generator: 33-47: × 80 = 37 ≈ 37 workers 300 3 85 2 Number each member from 1-100. Use a calculator or random number 48-62: × 80 = 22 ≈ 23 workers A variable that can take any value in a given range is a continuous 300 3 generator to generate 12 random numbers between 1-100. Select the members If the number of workers required is not a whole number, it is rounded off variable. A variable that can only take specific values is a discrete who correspond to the numbers. to the nearest whole number. variable. 3. Number the workers in each group. B) Lottery sampling: 4. Use a random number generator or table to produce the required In a grouped frequency table, the specific data values are not shown. Write the name of members on identical cards and place them in the hat. Draw quantity of random numbers. Class boundaries show the maximum and minimum values in up 12 cards and select these members. each group or class Advantages Disadvantages The midpoint is the average of class boundaries Advantages Disadvantages The class width is the difference between upper and lower Sample accurately reflects Population must be clearly classified into Free of bias Not suitable for large samples and population structure distinct strata class boundaries Easy and cheap for small samples populations Proportional representation Same disadvantages as simple random and populations Sampling frame needed of group within population sampling within each stratum Large data set Each sampling unit has a known and If you need to do calculations on large data sets in your exam, the equal chance of selection relevant extract will be provided. https://bit.ly/pmt-cc https://bit.ly/pmt-edu https://bit.ly/pmt-cc