Variance (σ2) in statistics is a measurement of the spread between numbers in a data set. That is, it measures how far each number in the set is from the mean and therefore from every other number in the set.
In investing, the variance of the returns among assets in a portfolio is analyzed as a means of achieving the best asset allocation. The variance equation, in financial terms, is a formula for comparing the performance of the Elements of a portfolio against each other and against the mean.
Variance is calculated by taking the differences between each number in the data set and the mean, then squaring the differences to make them positive, and finally dividing the sum of the squares by the number of values in the data set.
Variance is one of the key parameters in asset allocation, along with correlation. Calculating the variance of asset returns helps investors to develop better portfolios by optimizing the return-volatility trade-off in each of their investments.
Variance measures variability from the Average or mean. To investors, variability is volatility, and volatility is a measure of risk. Therefore, the variance statistic can help determine the risk an investor assumes when purchasing a specific security.
A large variance indicates that numbers in the set are far from the mean and from each other, while a small variance indicates the opposite. Variance can be negative. A variance value of zero indicates that all values within a set of numbers are identical.
Advantages and Disadvantages of Variance
Statisticians use variance to see how individual numbers relate to each other within a data set, rather than using broader mathematical techniques such as arranging numbers into quartiles. One drawback to variance is that it gives added weight to outliers, the numbers that are far from the mean. Squaring these numbers can skew the data.
The advantage of variance is that it treats all deviations from the mean the same regardless of their direction. The squared deviations cannot sum to zero and give the appearance of no variability at all in the data.
The drawback of variance is that it is not easily interpreted. Users of variance often employ it primarily in order to take the square root of its value, which indicates the standard deviation of the data set.
Types of Sampling
Sampling is defined as the process of selecting certain members or a subset of the Population to make statistical inferences from them and to estimate characteristics of the whole population. Sampling is widely used by researchers in market research so that they do not need to research the entire population to collect actionable insights.
Types of sampling
Probability Sampling
Probability sampling s a sampling method that selects random members of a population by setting a few selection criteria. These selection parameters allow every member to have the equal opportunities to be a part of various samples.
Probability Sampling is a sampling technique in which sample from a larger population are chosen using a method based on the theory of probability. This sampling method considers every member of the population and forms samples on the basis of a fixed process. For example, in a population of 1000 members, each of these members will have 1/1000 chances of being selected to be a part of a sample. It gets rid of bias in the population and gives a fair chance to all members to be included in the sample.
There are 4 types of probability sampling technique
Simple Random Sampling
One of the best probability sampling techniques that helps in saving time and Resources, is the Simple Random Sampling method. It is a trustworthy method of obtaining information where every single member of a population is chosen randomly, merely by chance and each individual has the exact same probability of being chosen to be a part of a sample.
Cluster Sampling
Cluster sampling is a method where the researchers divide the entire population into sections or clusters that represent a population. Clusters are identified and included in a sample on the basis of defining demographic parameters such as age, location, sex etc. which makes it extremely easy for a survey creator to derive effective inference from the feedback.
Systematic Sampling
Using systematic sampling method, members of a sample are chosen at regular intervals of a population. It requires selection of a starting point for the sample and sample size that can be repeated at regular intervals. This type of sampling method has a predefined interval and hence this sampling technique is the least time-consuming.
Stratified Random Sampling
Stratified Random sampling is a method where the population can be divided into smaller groups, that don’t overlap but represent the entire population together. While sampling, these groups can be organized and then draw a sample from each group separately.
Non-probability Sampling
Non probability sampling method is reliant on a researcher’s ability to select members at random. This sampling method is not a fixed or pre-defined selection process which makes it difficult for all elements of a population to have equal opportunities to be included in a sample.
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Variance is a measure of how spread out numbers are in a data set. A low variance indicates that the data points tend to be very close to the mean, while a high variance indicates that the data points are spread out over a large range of values.
Population variance is the variance of a population, which is the entire set of data points that are being studied. Sample variance is the variance of a sample, which is a subset of the population.
There are several different types of sampling, which are methods of selecting a subset of data points from a population. Simple random sampling is a type of sampling in which each data point in the population has an equal chance of being selected. Stratified sampling is a type of sampling in which the population is divided into groups, or strata, and then data points are selected from each stratum in proportion to the size of the stratum. Cluster sampling is a type of sampling in which the population is divided into clusters, and then data points are selected from each cluster. Systematic sampling is a type of sampling in which data points are selected from the population at regular intervals. Convenience sampling is a type of sampling in which data points are selected based on convenience, such as data points that are easy to access. Quota sampling is a type of sampling in which data points are selected to ensure that the sample represents the population in terms of certain characteristics, such as age, gender, or race. Judgment sampling is a type of sampling in which data points are selected based on the judgment of the researcher.
The type of sampling that is used will depend on the research question that is being asked. For example, if the research question is about the average height of people in a population, then simple random sampling would be a good choice. If the research question is about the average height of people in different age groups, then stratified sampling would be a good choice. If the research question is about the average height of people in different parts of the country, then cluster sampling would be a good choice. If the research question is about the average height of people who are easy to access, then convenience sampling would be a good choice. If the research question is about the average height of people who represent the population in terms of age, gender, and race, then quota sampling would be a good choice. If the research question is about the average height of people who are judged by the researcher to be representative of the population, then judgment sampling would be a good choice.
Variance is a useful measure of variability, and it can be used to compare different data sets. For example, if the variance of the heights of people in one city is higher than the variance of the heights of people in another city, then we can conclude that the heights of people in the first city are more spread out than the heights of people in the second city.
Variance can also be used to calculate the standard deviation, which is another measure of variability. The standard deviation is calculated by taking the square root of the variance.
Variance is a useful tool for data analysis, and it can be used to answer a variety of research questions.
What is a population?
A population is a group of individuals or objects that have a common characteristic. For example, the population of a country is all the people who live in that country.
What is a sample?
A sample is a subset of a population. For example, if you want to know the average height of people in a country, you could take a sample of 100 people and measure their heights.
What is sampling?
Sampling is the process of selecting a sample from a population.
What are the different types of sampling?
There are many different types of sampling, but some of the most common include:
- Simple random sampling: Each individual in the population has an equal chance of being selected for the sample.
- Stratified sampling: The population is divided into groups (strata) and then a random sample is selected from each group.
- Cluster sampling: The population is divided into clusters and then a random sample of clusters is selected.
- Systematic sampling: Every nth individual in the population is selected for the sample.
What are the advantages and disadvantages of different types of sampling?
Each type of sampling has its own advantages and disadvantages. Simple random sampling is the most basic type of sampling, but it can be difficult to implement if the population is large. Stratified sampling can help to ensure that the sample is representative of the population, but it can be more difficult to implement than simple random sampling. Cluster sampling can be less expensive than simple random sampling, but it can be less representative of the population. Systematic sampling is easy to implement, but it can be biased if the population is not evenly distributed.
What is the sampling distribution?
The sampling distribution is the probability distribution of a statistic calculated from a sample. For example, if you take a sample of 100 people from a population and calculate the average height, the sampling distribution of the average height is the probability distribution of all the possible average heights that you could get if you took 100 samples of 100 people from the population.
What is the central limit theorem?
The central limit theorem states that the sampling distribution of the mean of a variable is approximately normally distributed, regardless of the distribution of the variable in the population, as long as the sample size is large enough.
What is the standard error of the mean?
The standard error of the mean is a measure of the variability of the sampling distribution of the mean. It is calculated as the square root of the variance of the sampling distribution.
What is the confidence interval?
A confidence interval is a range of values that is likely to contain the true value of a population parameter. For example, if you want to estimate the average height of people in a country, you could calculate a confidence interval for the average height. The confidence interval would be a range of heights that is likely to contain the true average height of people in the country.
What is the level of confidence?
The level of confidence is the probability that the confidence interval contains the true value of the population parameter. For example, if you have a 95% confidence interval, then you are 95% confident that the confidence interval contains the true average height of people in the country.
What is the margin of error?
The margin of error is the half-width of the confidence interval. For example, if you have a 95% confidence interval with a margin of error of 2 inches, then you are 95% confident that the true average height of people in the country is between 68 inches and 70 inches.
Question 1
A population is a group of individuals or objects that have a common characteristic. A sample is a subset of a population.
Which of the following is not a type of sampling?
(A) Simple random sampling
(B) Stratified sampling
(C) Cluster sampling
(D) Variance sampling
Answer
(D) Variance sampling is not a type of sampling. The other three Options are all types of sampling.
Question 2
A simple random sample is a sample in which every individual or object in the population has an equal chance of being selected.
Which of the following is not a characteristic of a simple random sample?
(A) The sample is representative of the population.
(B) The sample is unbiased.
(C) The sample is random.
(D) The sample is easy to collect.
Answer
(D) A simple random sample is not necessarily easy to collect. The other three options are all characteristics of a simple random sample.
Question 3
Stratified sampling is a sampling method in which the population is divided into groups, or strata, and then a random sample is selected from each group.
Which of the following is not an advantage of stratified sampling?
(A) It can improve the accuracy of the results.
(B) It can reduce the cost of sampling.
(C) It can make the results more representative of the population.
(D) It can be difficult to implement.
Answer
(D) Stratified sampling is not necessarily difficult to implement. The other three options are all advantages of stratified sampling.
Question 4
Cluster sampling is a sampling method in which the population is divided into groups, or clusters, and then a random sample of clusters is selected.
Which of the following is not an advantage of cluster sampling?
(A) It can be less expensive than simple random sampling.
(B) It can be more efficient than simple random sampling.
(C) It can be more representative of the population than simple random sampling.
(D) It can be more difficult to analyze the results than simple random sampling.
Answer
(D) Cluster sampling is not necessarily more difficult to analyze the results than simple random sampling. The other three options are all advantages of cluster sampling.