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Statistics, in a broad sense is a mathematical science which deals with interpretation of data that has been collected, organized, analyzed, and presented. These data will then be used as a basis for inference to make crucial decisions. It is widely used in almost every field which includes social, business, psychology, agriculture, governmental, medicinal, and environmental. Business statistics being one of them primarily seeks to give better decision making in the face of uncertainty to any organization or individual. It is the use of data analysis tools from elementary statistics in business which helps the management and business owners to come with viable strategies for their business/company. To make such decisions there are some skills that are required in forecasting, product planning, personnel management, quality control, market research, and yearly reports by the individual who is strategizing for the company. Business statistics is applied extensively in finance, marketing, production, services and operations management.
Descriptive Statistics: It is a summarization or description of a data set which collects responses or observation from an entire population or a sample. It helps in getting in depth knowledge of the data set by looking into what and why something has happened. There is also a possibility of distortion or missing out on important information in large datasets which can be limited through descriptive statistics as it can run comparisons across different units or people. The principal advantage of descriptive statistics is that it helps in simplifying large amounts of data in a practical manner and they also form a basis for almost all quantitative analysis of data along with simple graphics analysis. There are different types of descriptive statistics such as:
Measures of Frequency: This measure helps in calculating or observing a particular value on how many numbers of times it has occurred in a dataset. All such variable and all possible values and frequencies associated with it are checked to rightly determine its distribution and pattern of frequencies. Frequency distributions can either show the exact number of observations in each range or it can be percentage of observations which is also known as relative frequency distribution. Additionally, frequency distribution table can be used for both numeric and categorical variables.
Measures of Central Tendency: It is at times also referred to as measures of central location because it focuses on the central position of a data within a particular data set. It estimates the centre or the average of a data set using the mean, median, and mode.
Mean: The Mean or M is the most popular and commonly used method to find the average which is why it is known as the mathematical average. It is often used with continuous data but it can also be used with discrete data as well. One of the chief properties of mean is that it decreases the error in predicting any one value in a dataset. However, mean should not be used when the values in the dataset are inconsistent by being particularly small or large numerical value, for example, wages of staff in a company. Therefore, mean is the most viable measure of central tendency to use for Interval/Ratio variable that are not skewed.
Median: Median is more specific as it is precisely in the middle of data set which has been organized according to the magnitude of values. Due to this, it is also known as the positional average. Hence, when mean cannot be used in the above-mentioned dataset, median could be used as it is less affected by deviations and skewed data. It is the best measure of central tendency to be used for both ordinal, and Interval/Ratio (skewed) variable.
Mode: Mode is frequently used and most popular among the measures of central tendency. It is the value that occurs regularly in a set of numbers. Through mode the most common category can be found in categorical data. Mode is the most viable measure of central tendency to use for nominal variable.
Measures of Dispersion or Variation: While a measure of central tendency helps in finding the typical value of a data, in measures of variability it represents the amount of deviation or dispersion in a data. It defines how disperse the data points are from the centre, with low dispersion indicating cluster of data points to the centre whereas high dispersion indicates that they fall further from the centre. The lower the variability the more consistent the dataset becomes. Through variability a sample’s diversity can also be assessed. The different measures of variability are listed below:
Range: It measures the extreme difference in value of a data in a dataset. However, it is sensitive to outliers (the values that are extremely high or low) and should not be used when it is present.
Variance: It uses the mean as the measure for the middle of distribution and then estimates the average degree of spread of the data to that mean. It is also commonly defined as average squared deviation from the mean.
Standard Deviation: Like variance, standard deviation also measures closeness of scores in a dataset to the mean. However, standard deviation is expressed in the same units as the initial values of a dataset. The standard deviation of a statistical population, data set, probability distribution, and sample is the square root of its variance.
Inferential statistics can be distinguished from descriptive statistics as the latter simply describes the data on what it is and what it is showing. Inferential statistics on the other hand helps in reaching conclusion by inferring from the sample data to make generalizations about the population. It helps in understanding what the population is thinking beyond the immediate data alone. Hence, it is mainly use for a sample size of a large group or population to derive estimates based on hypotheses testing method. Sample data is used for inferential statistics because it is both cost effective and less tedious as compared to collecting data from an entire population. However, if the sample used is not representative of the target population valid statistical inferences cannot be made. Hence, it is important to use random and unbiased sampling methods.
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Statistics is the science of collecting, analyzing, interpreting, and presenting data. It plays a pivotal role in various fields, from economics and biology to social sciences and engineering, helping professionals make informed decisions based on empirical evidence.
The two main branches of statistics are descriptive statistics, which summarizes and organizes data, and inferential statistics, which draws conclusions from data subject to randomness.
Studying statistics equips individuals with the skills to decipher complex datasets, make predictions, and understand patterns, making it invaluable in todays data-driven world. Moreover, with the rise of big data and advanced analytics, a foundation in statistics offers a competitive edge in numerous careers, enabling one to extract meaningful insights from raw information.
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