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Business statistics is a science and a branch of statistics that helps managers make decisions on the basis of statistical analysis of different business data and processes. It involves the application of basic statistical tools to a wide range of business scenarios including those related to production planning, forecasting, quality control, market research, and personnel management. **For example**: it can be used to forecast future volume of sales for the next quarter or year, estimate the **probability** of a certain defect in a product coming off the production line, and estimate the number of workers that will be required in the short and long terms. Most tools used in business statistics, such as **regression analysis** and **hypothesis testing** originate from basic mathematical concepts of **mean, median, mode**, probability, **bell curve** and bar graphs. Because statistics allows for a high degree of reliability of probable outcomes, it has become an integral part of the managerial decision-making process in the modern business environment which is often faced with the challenges of uncertainties and unpredictable events.

**SOME IMPORTANT STATISTICS HOMEWORK TOPICS:**

There are mainly two types of statistics used in business scenarios-**Descriptive Statistics and Inferential Statistics**.

As can be understood from the name, descriptive statistics is used to summarize and describe a given dataset in a coherent and meaningful manner. Descriptive statistics utilizes historical data to identify past achievements as well as issues or mistakes that affected performance of the business. This is why it is also sometimes called “cause and effect” analysis. It helps businesses observe and explain why a given event has occurred. For example, it can be used to understand why customers behave in a certain way and how they react to the products, prices and features being offered. The importance of business statistics can be seen in the fact that businesses often use it in making critical decisions relating to corporate deals, marketing strategy and budget, operations, and finance.

**Following are the descriptive statistics used by businesses:**

**Measures of Central Tendency:** Mean, Median, and Mode

**Measures of Position:** Quartile ranks and Percentile ranks.

**Measurements of Frequency:** Count, Frequency, and Percentage.

**Measures of Variation or Dispersion:** Range, **Variance and Standard Deviation**.

Inferential statistics is used to draw inferences or conclusions from the analysis of data. It makes assumptions about measuring parameters by taking a specific statistic from the given dataset. Sample data are generally used to solve various types of research problems.

**Following the types of inferential statistics applied in business situations:**

One Sample Test of Hypothesis

ANOVA or T-test

Chi-Square Statistics and Contingency Tables

Bivariate and Multivariate Regression

Confidence Interval

Pearson Correlation

The main areas of inferential statistics are hypothesis testing and parameter estimation.

Business managers and analysts often have to generate ideas about improving the performance of the business. They are required to develop innovative ways to improve, for example, sales and other important performance metrics. From observing routine activities, they may think that promoting a product in a certain manner will increase its sales. However, without hard statistical data to confirm this idea, it might just be random guesswork and it cannot be said with certainty whether it will work or not. Hypothesis testing is an effective method that business managers apply in such situations to back up their idea or claim (called a hypothesis) with hard data derived from relevant statistical tests. It is important to understand that for accuracy of the result, several considerations need to be made before testing a hypothesis. The significance level at which the result will be called accurate and the hypothesis will be accepted, and ensuring that the data is clean and high quality, are some of the important considerations in hypothesis testing. Hypothesis is one of the most complex and challenging areas of business statistics.

In parameter estimation, the analyst takes out a sample from the dataset (for example, 50 out of 100) and determines a relevant or required statistic for it. To understand the concept of parameter estimation, assume that the average wages of 100 workers in a factory is $20/hour. The manager will use this statistic (hourly wages) to infer that the average salary of a larger population of workers (say 1,000) is around $20/hour. He/she will understand that $20/hour may not be the exact salary of each worker and that it may range from say, $19-21. The estimated wages of $20 here is the statistic which is also called the confidence interval derived from the results of a test of hypothesis.

A sample is a part of a larger population, for example, 100 electric car owners out of total electric car owners in New York City. The sample can be used as a reference point to make conclusions about the entire population. Collecting a sample for business statistics is a complex and crucial task. To ensure that the data is high quality and representative of the entire population being studied, the sample must be selected very carefully and by using a rigorous method. Analysts cannot just select random, irrelevant items from the population to make up the numbers. There are several sampling methods used for business statistics, the most common of which are:

**Systematic Sampling:** Individual elements of the sample are selected from a list of participants that the analyst wants to include in the study.

**Simple Random Sampling:** Sample elements are selected randomly from the population so that each individual element of the population has the same probability of being included in the study.

**Cluster Sampling:** The population is divided into smaller clusters (groups) and random elements are then selected from each cluster to make up the sample. This method is used when the subsets or clusters are known but individual elements are not known to the analyst.

**Stratified Sampling:** The population is divided into homogenous subgroups in which the elements have very similar characteristics. Individual elements can only belong to one subgroup. Systematic sampling or simple random sampling method can then be used in each subgroup to select elements and create a combined sample.

Statistical analysis plays a crucial role in helping businesses understand where they stand, how they can maximize outputs and minimize costs, and what the future holds for them. It allows them to assess their past performance using several types of data to develop appropriate strategies and solve a variety of business problems. Some of the important applications of business statistics include:

**Decision-making:** Statistical analysis of data allows businesses to quantify their performance and identify existing and emerging patterns. Data-backed evidence of performance and issues helps managers make well-informed decisions for the future. Statistical insights help them understand the cause and effect of a given event or phenomena, thus providing quality information needed for developing rational business strategy.

**Performance management:** Measuring and evaluating performance of different units and activities is the most common application of business statistics. Using statistical tools, a small sample of a product can be studied to estimate the quality or the occurrence of a defect in the whole batch. The results can be used to determine whether the batch meets quality requirements or whether it needs to be discarded because of poor quality. Another application is to determine whether the production output of a plant matches its capacity. If the production is below the capacity, the management can identify and address the shortcomings which may be in the form of inadequate training of workers, adjustments in the machinery, etc.

**Market research:** Businesses regularly use statistics to identify the market and potential for a new product before producing it in bulk quantities. Techniques such as random surveys of target customer groups allow them to understand whether the product will be accepted or rejected once launched. High interest shown by potential customers can motivate the business to invest in production while low interest can save them from investing in a potentially failed product.

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