Statistics for Business Decisions
Statistics is the process of collecting, processing and analyzing the data for the purpose of assisting the process of decision making. It has application in various fields ranging from biology, demographics, economics, business and other scientific and social domains. However, statistics also suffers from some limitations including ignoring of qualitative aspects or the study of individuals (as it deals with aggregates). It can also be manipulated and results be misstated.
Primary data refers to first hand data collected by the researcher. On the other hand, secondary data refers to the data collected by someone else, such as data published by the census. Statistics involves classification and presentation of data. The various modes of classification include tabulation of data. Graphical presentation of data is done through various means such as bar diagram, histogram, frequency polygon and ogive.
Measures of Central Tendency
One of the important aspects of statistics is the measurement of central tendency of a set of data. These measures are:
- Mode: the most frequently occurring observation in the data set
- Arithmetic Mean: the average obtained by dividing the sum of observations by the number of observations
- Geometric Mean: the nth root of the product of the observations
- Harmonic Mean: the number of observations divided by the sum of reciprocals of the observations.
- Median refers to the mid-point of the given set of observations and mode refers to the most frequent observation in the data.
All these measures have their own applications and limitations.
Measures of Dispersion
Dispersion refers to the variability or scatter of the data about its central values.
The various measures of dispersion include:
- Range (difference between highest and lowest observation,)
- Quartile deviation (difference between the upper and lower quartile divided by 2),
- Mean deviation (deviation of the individual observations about the mean) and
- Standard deviation (square root of variance).
Skewness depicts the scatter of a data about its mean value. Kurtosis refers to the peakedness (or height) of the frequency distribution.
The probability of any event is the chance of the happening of that event in a certain experiment. The various types of events include impossible events (probability=0), simple events, compound events, dependent and independent events, mutually exclusive events, and mutually exhaustive events.
Some of the major theorems of probability are conditional probability and Bayes theorem. Conditional probability give the probability of an event A given that event B has already occurred. Bayes theorem is used to calculate probability based on the probability of each cause of the event and the conditional probability of the outcome of each of the causes. Probability Distribution is a tabular presentation, which specifies the probability associate with each possible outcome of a random experiment.
The two major types of random variable are discrete and continuous random variables. A discrete random variable is the one that can take only specific countable values while a continuous random variable can take any value within the specified range.
The mathematical expectation of a random variable is the probability weighted average obtained from the probability distribution.
Binomial distribution is a discrete probability distribution of the number of successes in a series of independent experiments. Poisson distribution shows the probability of a given number of events during a given period of time. Normal distribution is a continuous probability distribution in which most values cluster in the middle and taper off symmetrically on both sides.
Since it is not always feasible to study the entire population, sampling is used to select a portion of the population to be studied so that the results can be generalized for the entire population.
The two types of sampling are:
- Probability sampling: where the sample is selected such that it is representative of the population
- No Probability Sampling: where the sample is not representative as it is influenced by personal bias.
The 2 types of probability sampling are random and stratified sampling, while non-probability sampling includes quota, purposive and convenience sampling.
The confidence interval is the range in which the population parameter will lie at a certain level of confidence. Test of Hypothesis is conducted to test if a given statement about the sample can be considered true for the entire population. Z test is used to determine if the two means are different when the population variance is known and sample size is large, while t test is used to test means when population variances are not known and the sample size is small. F test is used for analysis of variance where the test statistic follows the F-distribution. The chi-square test is used to find the goodness of fit between the observed and expected data.
Correlation and Regression Analysis
Correlation is a statistical measure describing the degree of relationship among variables. Regression analysis is used to mathematically model the relationship among the dependent and one or more independent variables. These are considered as related concept as both these deal with relationships among variables.
The various methods of estimating linear correlation are scatter diagram, Karl Pearson’s correlation coefficient, Spearman Ranks correlation and the concurrent deviation method. Partial correlation measures the correlation between variables considering the effect of other factors as constant. Multiple correlation shows the values of a dependent variable from the linear function of other independent variables.
Single Linear Regression Model shows the effect of only one independent variable while a Multiple Linear Regression Model captures the effect of two or more independent variables on the dependent variable. Linear regression analysis is based on calculation of OLS estimators of the intercept and slope coefficients which fulfil the property of BLUE estimators (Best, Linear, Unbiased, Efficient estimators).
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Time Series Analysis
Interpolation refers to determining the value of a function between the given discrete values. Extrapolation refers to tabulating the value of a variable outside the observed range. The graphical and linear approximation method is used for the purpose of interpolation and extrapolation. Interpolation is widely used in financial analysis (such as, calculating unknown price or yield of security, determining interest term of a yield, etc.).
Index Numbers are used in economic analysis to present price or quantity as compared with a base or standard value. In weighted index numbers, weight is assigned to each commodity relative to its importance. Un-weighted index numbers does not assign any weights, thereby giving equal importance to all commodities. Quantity index measures the relative change in quantity over a period of time and value index presents the value of economic aggregates over the time period. The consumer price index measures the price level of a market basket of consumer goods.
Time series is a series of data measured over discrete measure of time. The various components of time series are: trend, seasonal variation, cyclical variations and the irregularity. These components are expressed either as a sum (additive model) or the other three components are measured as a proportion of the trend (multiplicative model) the most popular method of trend analysis is the ordinary least squares approach. Moving averages are used to analyze data by creating averages of subsets of the data. The carious moving averages are: Simple Moving Average (SMA), Weighted Moving Average (WMA), and Exponential Moving Average (EMA).
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Statistics is studied by majorly all college students and university graduates. Statistical analysis forms an important part of business, finance and economics study programs. Students of all business majors are required to study a course in statistical decision making as well as advanced courses on econometrics and financial econometrics. Understanding of statistical decision making can help business students to in conducting economic analysis, sales forecasting, cost and distribution optimization, quality assurance, Risk Management as well as time series forecasting for seasonal trends and variations in profit/loss.
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