In statistics, a population is a set of similar items or events which is of interest for some question or experiment.
- Population is a huge material.
- Population may be infinite or finite. If a population consists of fixed number of values, it is said to be finite. If population consist of an endless succession of values, the population is an infinite one.
Example: Birth weights of all babies in a particular hospital in month November, the monthly expenditure of non-residential students of 2nd year in Department of Botany etc.
A sample is a smaller group of members of a population selected to represent the population.
In statistical inference, a subset of the population (a statistical sample) is chosen to represent the population in a statistical analysis. If a sample is chosen properly, characteristics of the entire population that the sample is drawn from can be estimated from corresponding characteristics of the sample.
- Size of the sampling depends on population size.
It may be defined as a part of a population.
- The process of selecting samples from a population is called Sampling.
- Inference about the population is drawn from studying sample.
Random Sampling: Selecting samples being unbiased is called random sampling. An important feature of a good study is that the sample is randomly selected from the target population. Randomly means that every member of the target population has an equal chance of being included in the sample. In other words, the process you use for selecting your sample can’t be biased.
Its important because if you select your subjects in a way that is biased-then your results will also be biased. And more likely, it wouldn’t represent the population.
Suppose you’re conducting a phone survey on job satisfaction of Bangladeshis. If you call them at home during the day between 9 a.m. and 5 p.m. you’ll miss out all those who work during the day; It could be that day workers are more satisfied than night workers.
Or your boss told you to make a survey of the overall development of the office from the year 2010 to 2020. To make your boss happy while sampling you chose the things as samples which actually developed but didn’t count those which almost remained the same or demoted in 10 years.
Like the above two examples there are many ways of being biased. To get a good survey its necessary to avoid all kinds of biasness possible.
Mahajan BK 2002.(Methods in Biostatistics)(6th edition)
Deborah Rumsey (Statistics for Dummies)
You’re interested in the percentage of female versus male shoppers at a department store. So one Saturday morning, you place data collectors at each of the store’s four entrances for three hours, and you have them record how many men and women enter the store during that time.
1. Why can collecting data at the store on one Saturday morning for three hours cause bias in the data?
- It assumes that Saturday shoppers represent the whole population of people who shop at the store during the week.
- It assumes that the same percentage of female shoppers shop on Saturday mornings as any other time or day of the week.
- Perhaps couples are more likely to shop together on Saturday mornings than during the rest of the week, bringing the percentage of males and females closer than during other times of the week.
- The subjects in the study weren’t selected at random.
- All of these choices are true.
Ans: E. All of these choices are true.
Bias is systematic favoritism in the data. You want to get data that represents all customers at the store, no matter what day or what time they shop, whether they shop in couples or alone, and so on. You can’t assume that the people who shopped during those three hours on that Saturday morning are representative of the store’s total clientele. This sample wasn’t drawn randomly — everyone who walked in was counted.
Statistic & Parameter
Parameter is a summary value that describes the population such as its mean, variance, correlation coefficient, proportion etc.
- It is a characteristic of a population.
Statistic is a summary value that describes the sample as its mean, standard deviation, standard error, correlation coefficient, proportion etc.
- It is a characteristic of sample.
The value is calculated from the sample and is often applied to population but may or may not be a valid estimate of population. There is a good reason that the population parameter and sample static will vary; hopefully very less but can be significant too if the sample is biased or too small (i.e. doesn’t represent the population properly).
Your interested in knowing what percent of all households in a large city have a single woman as the head of the household. To estimate this percentage, you conduct a survey with 200 households and determine how many of these 200 are headed by a single woman.
1. In this example,what is the population?
2. In this example,what is the sample?
3. In this example, what is the parameter?
4. In this example, what is the statistic?
1. Ans: All households in the city.
A population is the entire group you’re interested in studying. The goal here is to estimate what percent of all households in a large city have a single woman as the head of the household. The population is all households, and the variable is whether a single woman runs the household.
2. Ans: Selected 200 households.
The sample is a subset drawn from the entire population you’re interested in studying. So in this example, the subset is the 200 households selected out of all the households in the city.
3. Ans: The percent of households headed by single women in the city.
A parameter is some characteristic of the population. Because studying a population directly isn’t usually possible, parameters are usually estimated by using statistics (numbers calculated from sample data).
4. Ans: The percent of households headed by single women among the 200 selected households.
The statistic is a number describing some characteristic that you calculate from your sample data; the statistic is used to estimate the parameter (the same characteristic in the population).
Ref: Statistics: 1,001 Practice Problems For Dummies