Statistics: Scope, Applications, and Techniques

Posted on May 12, 2024 in Mathematics

Scope of Statistics

Through statistical analysis, business executives gain insights into market trends, customer demands, and purchasing patterns. This knowledge guides product development, marketing strategies, and customer relationship management, ensuring sustained growth and competitiveness.

Statistics is the discipline that concerns the interpretation, analysis, organization, collection, and presentation of data. The scope of Statistics is very immense, the application of statistics goes into diverse fields such as solving social problems, industrial and scientific problems.

Skewness and Kurtosis

Skewness and Kurtosis are statistical measures used to describe the shape and characteristics of a distribution in statistics. Skewness is a measure of symmetry (or, more specifically, the lack of symmetry in the data set), which can be positive or negative. In contrast, Kurtosis measures the tailedness of a distribution (i.e., it quantifies the extremity of outliers in the distribution).

Skewness defines the shape of the distribution. Usually, we get a lot of asymmetric distributions, and these distributions have unevenly spread data. There are two types of skewness – positive or right-skewed and negative or left-skewed

Kurtosis is a statistical measure that describes the degree of peakedness or flatness of a distribution. It measures the shape of the distribution, specifically the height and sharpness of the central peak, relative to that of normal distribution. It is the fourth moment of statistics.

The term “Kurtosis” comes from the Greek word “Kurtos”, which means curved. 

Kurtosis is useful to identify the potential outliers in a dataset, as distributions with high kurtosis have more extreme values than normal distributions.

There are three types of Kurtosis: Mesokurtic, Leptokurtic, and Platykurtic.

Standard Deviation

The standard deviation is a measure of how spread out the values in a dataset are. It quantifies the amount of variation or dispersion of a set of values. It is widely used because it takes into account the distance of each data point from the mean. Other measures of dispersion include the range, variance, and interquartile range. The range is the difference between the largest and smallest values in a dataset, while the variance is the average of the squared differences from the mean. The interquartile range is the range covered by the middle 50% of the data. Each of these measures has its own strengths and weaknesses, and the choice of which one to use depends on the specific characteristics of the dataset and the goals of the analysis.

The standard deviation takes all data into consideration because it uses all the observation in its computation.

Standard Deviation is considered as the best measure of dispersion as, Help to make comparison between the distribution of two or more different datasets. Based on all values. Capable of further algebraic treatment.

Functions of Statistics

Functions of statistics, like summarizing data, testing hypotheses, and making predictions, enable informed decision-making in various fields. They provide a structured approach to analyzing, interpreting, and communicating information, making complex data more understandable. In essence, statistics functions are essential tools for uncovering patterns, trends, and insights, aiding in problem-solving, informed policy development, and better-informed choices in science, business, and everyday life.

The important functions of statistics are: Statistics helps in gathering information about the appropriate quantitative data. It depicts the complex data in graphical form, tabular form and in diagrammatic representation to understand it easily. It provides the exact description and a better understanding.

To Test Hypothesis

To Make Predictions

To Identify Patterns and Trends

To Solve Problems

To Design Experiments

To Analyze Data

To Interpret Results

To Communicate Findings

Positive and Negative Correlation

In statistics, correlations describe relationships that exist between two or more things. There are multiple types of correlations, including positive correlations and negative correlations. Understanding these two types of connections can help you compare data sets effectively and draw meaningful conclusions.

  • A positive correlation exists when two variables operate in unison so that when one variable rises or falls, the other does the same.
  • A negative correlation is when two variables move opposite one another so that when one variable rises, the other falls.
  • Correlations can help marketers, supply chain managers and other professionals by identifying useful patterns, like correlations in customer behavior or industry-specific practices.
  • Positive and negative describe the type of correlation, or relationship, that exists between two variables or information sets. Using a correlation coefficient, you can determine if your data relates either positively or negatively. Sometimes, you might see the correlation coefficient represented with the letter”p” It is important to remember that the correlation coefficient is most reliable when the relationship between your two sets of figures is linear, rather than curved, for instance.
  • If one set of information increases when the other increases, that is a positive correlation. If you plot your data on a graph, a positive correlation would typically show a line extending from the lower-left corner of your chart toward the top right.
  • If one set of information decreases when the other increases, it is a negative correlation. Negative correlations usually look somewhat like a line extending from the chart’s top left to the bottom right. Negative correlations work the same way as positive ones, but their correlation coefficients are less than zero. A perfect negative correlation would have a correlation coefficient of -1.

Methods of Measuring Trend in Time Series

1) Graphic Method

2) Method of semi averages

3) Method of curve fitting by principle of least square

4) Method of moving averages

Graphical method, also known as ‘free hand curve fitting’, is the most simplest and flexible method for measurement trend component. This method is based on a free hand moving curve. This smooth hand curve are plotted on the values of study variable value with respect to time interval of any time series.

Method of semi averages eliminates some biasedness that prevail in the graphical method. In this method, we divide whole time series into two semi parts and take their average for obtaining trend line

Method of moving average method is very simple and flexible method for measuring the trend line by means of moving average of successive groups of the time series. This average process remove the fluctuation of the given time series.

The principle of least square is a mathematical analysis device and most widely used method to fit a trend for a given time series. It is mostly used in cases where time series observation value’s relationship with time is very strong, this relationship shows the tendency of increment and decrement with an increase in the value of time then this method is most appropriate to get a reliable future forecast value. This method is used for all type of trends i.e. linear and non-linear

Technical Problems Associated with Time Series

The three main machine learning problems with time series are forecasting, classification, regression, and anomaly detection. In this section, we’ll provide a broad overview of applications of time series and a history of machine learning and analysis techniques applied to time series.

Common problem scenarios when dealing with time series data include:

  • Forecasting: The use of a model to predict future values based on previously observed values. This technique is used to predict future values of the time series based on past values. This can be done using methods such as ARIMA or exponential smoothing.
  • Decomposition: This technique is used to separate the data into its constituent parts such as trend, seasonality, and residuals. This can be done using methods such as additive or multiplicative decomposition. This involves trend analysis, where we identify long-term trends in a time series, and seasonality analysis, which is about identifying repeating patterns in a time series.
  • Classification/Regression: This technique is used to predict a target variable based on the time series data. This can be done using methods such as support vector machines or logistic regression.
  • Anomaly detection: Identifying unusual patterns (outliers) in a time series. Outliers are unusual observations that fall outside of the typical pattern.
  • Clustering: This technique is used to group together similar time series. This can be done using methods such as k-means clustering.
  • Drift detection: This technique is used to identify systematic changes in the time series data. This can be done using methods such as the Mann-Kendall test.
  • Smoothing: This technique is used to remove the noise from the data. This can be done using a simple moving average or a more sophisticated technique such as exponential smoothing.


GEOMETRIC MEAN

Define geometric mean.

The main advantage of the geometric mean are :

  1. The calculation is based on all the terms of the sequence.
  2. Suitable for further mathematical analysis.
  3. Fluctuations in the sample do not affect the geometric mean.
  4. It gives more weight to small observations.

The disadvantage of the geometric mean are :

  1. One of the main drawbacks of the geometric mean is that if one of the observations is negative, the geometric mean will be imaginary, despite the other set of observations.
  2. Due to the complexity of the numbers, it is not easy for anyone other than a mathematician to understand and calculate.

USES OF STATISTICS IN BUSINESS

One can understand the importance of Statistics in business from the following:

(i) Marketing – Statistical analysis is frequently used in providing information for making decisions in the field of marketing. It is necessary first to find out what can be sold and then to evolve suitable strategy, so that the goods reach to the ultimate consumer. A skilful analysis of data on production purchasing power, man power, habits of consumers, habits of consumer, transportation cost should be considered to take any attempt to establish a new market.

(ii) Production – In the field of production statistical data and method play a very important role. The decision about what to produce, how to produce, when to produce, and for whom to produce is based largely on statistical analysis.

(iii) Finance – The financial organization discharging their finance function effectively depend very heavily on statistical analysis of peat and tigers.


(iv) Banking – Banking Institute has found it increasingly necessary to establish research department within their organization for the purpose of gathering and analysis information, not only regarding their own business but also regarding the general economic situation and every segment of business in which they may have interest.

(v) Investment – Statistics greatly assists investors in making clear and valued judgment in his investment decision in selecting securities which are safe and have the best prospects of yielding a good income.

(vi) Purchase – The purchasing department in discharging their function makes use of statistical data to frame suitable purchase policies such as what to buy; What quantity to buy; What time to buy; Where to buy; Whom to buy;

(vii) Accounting – Statistical data are also the employer in accounting particularly in auditing function, the technique of sampling and destination is frequently used.

(viii) Control – The management control process combines statistical and accounting method in making the overall budget for the coming year including sales, materials, labour and other costs and net profits and capital requirement.