About Sampling
Statistics, or what we refer to as ‘Stats’ in common parlance, is quite a useful branch of mathematics that can aid in analyzing and solving myriad everyday problems. It has a wide range of applications in different fields, right from medicine, and sports, to engineering, etc. Now let us know more about it.
The advantages of statistics include collecting data in the form of numerical figures, grouping and presenting the data, analyzing and interpreting the data, and arriving at novel information curated from the data. Within the branch of mathematics, statistics is a very important concept to learn. A branch of statistics also deals with analyzing certain scenarios in a macroscopic way where we work with a given population and a sample.
Population refers to a group of people or objects as a whole, while a sample is a subset of the whole. By examining samples of a population, you can learn more about that population.
The above diagram shows population.
↓
The diagram below shows a sample of the above population.
There are two types of samples
1) An unbiased sample
2) A biased sample
- An unbiased sample represents the population. It is chosen at random and is large enough to provide reliable information.
- A biased sample does not represent the population. One or more groups of people are given preferential screening.
An unbiased sample’s results are proportional to the population’s results. Therefore, unbiased samples can be used to draw conclusions about a given population. Samples that are skewed are not representative of the population. So, you cannot not use them to make conclusions about the population.
Example 1: Suppose you want to estimate the number of students in a college who come to college by bus. In this case, which of the following samples is unbiased?
A. 5 students in the hallway
B. All students on the football team
C. 26 senior year students at random
D. 81 students at random during lunch
Solution:
Choice A: It is insufficiently large to provide accurate data.
Choice B: It isn’t chosen at random.
Choice C: Since senior year students are given preference over other students, this sample is not representative of the population. Conclusions made from the sample in choice C may be inaccurate because senior year students are more likely to drive to school in their cars.
Choice D: Since this was chosen at random, it is representative of the population and large enough to provide accurate data.
So, the correct answer is D.
Example 2: Suppose you want to know how your classmates feel about having a science fair. In such a case, determine whether each of the following conclusions is valid.
A. You survey the 50 classmates who want the science fair in the month of march. The diagram shows the results. You conclude that 40% of your classmates support the idea of having the science fair in March.
B. You survey the 50 classmates at random. The table shows the results. You conclude that 70% of the classmates of your class do not support the idea of the science fair due to insufficient time left for exam preparations.
Classmates | Percentage out of 50 classmates in a class |
Supporters | 30% |
Non-supporters | 70% |
Solution:
A. The sample is not representative of the classmates because the results showed that there are some classmates who supported others just owing to the fact the examinations were to be held soon; they may be less likely to support it. As a result, the sample is skewed, and the conclusion is unreliable.
B. Since the sample was chosen at random and is large enough to provide accurate information, it is representative of the classmates. As a result, the sample is fair, and the conclusion is correct.
Sampling is a central concept in statistics. It is usually impossible to examine every single element in a given population. As a result, research and media articles frequently refer to a ‘sample’ of a population. A graph of sample proportions for many different samples is the sampling distribution of the sample proportion.
Read More:
A) Another important concept in statistics is called population characteristics. When data from a population is used to calculate a numerical summary, its value is referred to as population characteristics.
B) When data from a sample is used to calculate a numerical summary, the value is called a sample statistic. Sample statistics can be used to ascertain the characteristics of a population.
C) A population characteristic is a summarized measure that describes a particular feature of the population, the entire set of things, or objects from which data might be collected. A summarized measure that describes a particular feature of a subset of the population is known as a sample statistic.
For example, the population could include all the students in the school, with the month in which the majority of the students were born as a population characteristic. A sample of students could be those who had mathematics during the fifth block of their schedules, with grade point averages is a sample statistic.
For each of the following questions, describe how you would collect data to answer the question and describe whether it would result in a sample statistic or a population characteristic.
A) What should the eighth-grade’s class trip destination be?
All eighth-grade students would be surveyed. The result would be a population characteristic.
It is possible that only those students who are in a particular classroom or students under a specific teacher would be polled. A sample of students would be surveyed, and the result would be a sample statistic
B) What is the average number of pets per family for your town’s residents?
Families responding to a survey at a local grocery store would provide the data. A sample of data would be used, and the outcome would be a sample statistic.
It’s possible that a town is small enough to poll every pet-owning family. If this is the case, the people polled are the general public, and the result is a population characteristic.
C) What percentage of people would see an improvement in their cholesterol levels if they tried a new diet?
People at a local health center would be polled for information. Those who were surveyed while on the new diet would be a sample, and the results would be a sample statistic.
It is possible that everyone involved with the new diet was tracked down and agreed to participate in the survey. The population would then be surveyed, and the outcome would be a population characteristic.
D) What is the average grade point of students admitted to a specific state university?
The information would typically come from the cumulative grade point averages of all freshmen at a given state university. As a result, a population characteristic would emerge.
It is possible that only a small number of students who registered or applied were surveyed. A sample of students would respond to the survey, and the result would be a sample statistic.
E) What is the average number of home runs hit by major league baseball players in a given season?
This answer would be derived from a population characteristic analysis of all major league hitters for that season.
Population refers to a group of people or objects as a whole. A sample is a portion of a larger whole. By examining samples of a population, you can learn more about that population.
The advantages of statistics include collection of data in the form of numerical figures, grouping and presenting the data, analyzing and interpreting the data, and arriving at new information from the data are the advantages of statistics.
There are two types of samples: Unbiased sampling, Biased sampling.
Unbiased sample is representative of the population. It is chosen at random and is large enough to provide reliable information. Biased sample is not representative of a population. One or more groups of people are given preferential screening.
An unbiased sample’s results are proportional to the population’s results. As a result, unbiased samples can be used to draw conclusions about a population
Samples that are skewed are not representative of the population. So, you should not use them to make conclusions about the population.
Sampling is a central concept in statistics. It is usually impossible to examine every single element in a population. As a result, research and media articles frequently refer to a ’sample’ of a population.
population characteristic is a summarized measure that describes some feature of the population, the entire set of things or objects from which data might be collected. A summarized measure that describes a feature of a subset of the population is known as a sample statistic.