Variance
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.