Business Statistics Full Notes

UNIT – 1 Introduction to Statistics What are statistics? a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data Importance of Statistics        Statistics helps in Planning Statistics helps in Mathematics Statistics helps in Economics Statistics helps in Trade Statistics helps in Research Work Statistics helps in weather forecasting Statistics helps in Insurance Limitations of Statistics  Statistics are aggregates of facts, so a single observation is not a     statistic, it deals with groups and aggregates only are best applicable to quantitative data. does not deal with individual items. If sufficient care is not exercised then statistical results might be misleading. a person who has an expert knowledge of statistics can handle statistical data efficiently. Some basic terms  Population: In statistics, population refers to the total set of observations that can be made. For example, if we are studying the weight of adult women, the population is the set of weights of all the women in the world. There are two different types of       population – finite and infinite. The finite population is also known as a countable population in which the population can be counted. The infinite population is also known as an uncountable population in which the counting of units in the population is not possible. Variable: A characteristic about each individual element of a population or sample. Data (singular): The value of the variable associated with one element of a population or sample. This value may be a number, a word, or a symbol. Data (plural): The set of values collected for the variable from each of the elements belonging to the sample. Experiment: A planned activity whose results yield a set of data. Parameter: A numerical value summarizing all the data of an entire population. Statistic: A numerical value summarizing the sample data. Statistical Methods Descriptive Statistics Inferential Statistics Descriptive Statistics –  It involves collecting, presenting and Characterizing of data  Its purpose is to describe data  Descriptive statistics summarize and organize characteristics of a data set. Inferential Statistics –  Involves Estimation and Hypothesis Testing  Purpose is to a Make decision about population characteristics  Inferential statistics takes data from a sample and makes inferences about the larger population from which the sample was drawn.  Inferential statistics is to draw conclusions from a sample and generalize them to a population, we need to have confidence that our sample accurately reflects the population. VARIABLES:  Qualitative variables are those Variables that are not numerical.  For example, eye colour like blue, green, brown  Quantitative Variables are those variables whose values result from counting or measuring something. Examples: height, weight, time  Qualitative variables can be further divided in nominal and ordinal and quantitative variables can be further divided in Discrete and Continuous o Nominal Variable: A qualitative variable that categorizes (or describes, or names) an element of a population. o Ordinal Variable: A qualitative variable that incorporates an ordered position, or ranking. o Discrete Variable: Discrete variables are numeric variables that have a countable number of values between any two values. A discrete variable is always numeric. For example, the number of customer complaints or the number of flaws or defects. o Continuous Variable: Continuous variables are numeric variables that have an infinite number of values between any two values. A continuous variable can be numeric or date/time. For example, the length of a part or the date and time a payment is received. Data and types  Data are the facts and figures collected, analysed and summarized for presentation and interpretation.  different types of data can be collected for different purposes. The data can be collected in connection with time or geographical location or  There are two types of data – quantitative and Qualitative  Qualitative data is non-statistical and This data isn’t necessarily measured using hard numbers used to develop graphs and charts. Instead, it is categorized based on properties, attributes, labels, and other identifiers.  quantitative data is statistical and This data type is measured using numbers and values, making it a more suitable candidate for data analysis. Category of data Primary data Secondary data It is the type of data that is It is the data that has already collected by researchers directly been collected through primary from main sources sources and made readily available for researchers to use for their own research. An example of primary data is An example of secondary data is the national census data collected the data collected from online by the government sources. primary data and collection methods  DIRECT PERSONAL INTERVIEWS - The investigator personally meets concerned individuals and collects the required information from them. When the area to be covered is vast, this method may prove very costly and time-consuming. Still, this method is concerned useful for certain laboratory experiments or localized inquires. Due to the personal bias of the investigator, errors are likely to influence the results.  INDIRECT PERSONAL INTERVIEWS - We interview the third parties or witnesses having information, whenever the direct sources do not exist, or the informants hesitate to respond for some reason or other.  QUESTIONNAIRES - The questionnaires are usually sent by mail to inquire through several pertinent questions. In questionnaires, there is a space for entering the asked information asked. The informants are requested to return the questionnaires to the investigator within a certain period. This method is cheap, reasonably expeditious, and good for extensive inquiries. However, only a small percentage of recipients respond to questionnaires if there is no incentive involved.  COLLECTION THROUGH ENUMERATORS - In this method, trained enumerators collected the information. They assist the informants in making the entries in the schedules or questionnaires correctly. If the enumerator is well trained, experienced, and discreet, then you can get the most reliable information through this method. Enumerator driven approach works best for a large scale governmental or an organizational inquiry. Private individuals or institutions cannot adopt this method as its cast would be prohibitive to them.  LOCAL SOURCES - In this method, the agents or local correspondents collect and send the required information, using their judgment as to the best way of obtaining it, but there is no formal collection of data. This method is cheap and expeditious but gives only the estimates Advantages and Disadvantages of primary data Advantages –  Applicable and usable – if done right  Accurate and reliable – can answer your direct research questions  Up-to-date – as you have collected the data Disadvantages –  Expensive  Not immediately available – takes time to define problem, sampling frame, method and analysis.  Not as readily accessible Secondary data  Secondary data is the data that have been already collected by and readily available from other sources. Such data are cheaper and more quickly obtainable than the primary data Advantages of Secondary data –  It is economical. It saves efforts and expenses.  It is time saving.  It helps to make primary data collection more specific since with the help of secondary data, we are able to make out what are the gaps and deficiencies and what additional information needs to be collected.  It helps to improve the understanding of the problem.  It provides a basis for comparison for the data that is collected by the researcher. Disadvantage of secondary data –  Accuracy of secondary data is not known.  Data may be outdated. CLASSIFICATION It is a process of arranging things or data in groups or classes according to their resemblances and affinities. It is the process of arranging data into sequences and groups according to their common characteristics or separating them into different but related parts. Characteristics of classification  performs homogeneous grouping of data  brings out points of similarity and dissimilarities.  may be either real or imaginary  flexible to accommodate adjustments types of classification  Geographical - based on the geographical regions.  Chronological - data are classified according to the time of its occurrence  Qualitative - classified according to the presence or absence of attributes in given units. Thus, the classification is based on some quality characteristics / attributes.  Numerical - based on quantitative measurements of some characteristics, such as age, marks, income, production, sales etc. Data Organization the method of classifying and organizing data sets to make them more useful RAW DATA Data recorded in the sequence in which they are collected and before they are processed or ranked are called raw data. Data Organization requires 2 major steps: Forming an array and Creating a frequency distribution table. Array  If a set of data is organized in either ascending or descending order, an array is formed. From the array, one can get some useful information, such as the lowest and the highest data value.  Advantages can be - Quick look at the highest and lowest observations, dividing data into various sections or parts, to identify any value appears more than once in the array  Disadvantages can be - Difficult form of presentation, neither summarizes nor organizes the data Fails to highlight the primary characteristic of the data Frequency distribution - Table that arranges data into several classes. The number of observations in each class is referred to as frequency denoted by Types of Frequency distribution –  Cumulative - Cumulative frequency distribution is a form of a frequency distribution that represents the sum of a class and all classes below it. It has two types – less than and more than  Relative and Percentage - Divide each class frequency by the total number of observations in the entire distribution and Multiply relative frequency by 100 UNIT -2 Measures of Central Tendency  Measures of Central Tendency are usually called as averages  Five measures of central tendency are – Arithmetic mean, median, mode, geometric mean, harmonic mean and weighted mean MEAN  Locates the centre of distribution  Most common measure and known as arithmetic mean  Mean is simply the sum of values divided by total number of items in set  X= X1 + X2 + X3 + X4 …. Xn / n  Merits - easy to understand and calculate Based upon all the observations Capable of further mathematical treatment Different series and different methods  Individual series – shortcut method Direct method – X = ΣX/n  Discrete Series – Shortcut method Direct Method  Continuous series - Shortcut method Direct method Step-Deviation method Formulas for mean Individual series  Direct method X= ΣX/n X – Mean ΣX – Sum total of column X N – number of observations  Short-cut method X= A+ ΣDX/N A – assume mean DX = X -A N- number of observations Discrete Series