Qualitative informations is a categorical measuring expressed non in footings of Numberss. but instead by agencies of a natural linguistic communication description. In statistics. it is frequently used interchangeably with “categorical” informations. For illustration: favourite colour = “yellow”
tallness = “tall”
When the classs may be ordered. these are called ordinal variables. Categorical variables that justice size ( little. medium. big. etc. ) are ordinal variables. Attitudes ( strongly disagree. disagree. impersonal. agree. strongly agree ) are besides ordinal variables. nevertheless we may non cognize which value is the best or worst of these issues. Note that the distance between these classs is non something we can mensurate. Quantitative dataQuantitative information is a numerical measuring expressed non by agencies of a natural linguistic communication description. but instead in footings of Numberss. However. non all Numberss are uninterrupted and mensurable. For illustration. the societal security figure is a figure. but non something that one can add or deduct.
For illustration: favourite colour = “450 nm”
tallness = “1. 8 m”
Quantitative informations ever are associated with a scale step. Probably the most common graduated table type is the ratio-scale. Observations of this type are on a graduated table that has a meaningful zero value but besides have an equidistant step ( i. e. . the difference between 10 and 20 is the same as the difference between 100 and 110 ) . For illustration. a 10 year-old miss is twice every bit old as a 5 year-old miss. Since you can mensurate zero old ages. clip is a ratio-scale variable. Money is another common ratio-scale quantitative step. Observations that you count are normally ratio-scale ( e. g. . figure of doodads ) . A more general quantitative step is the interval graduated table. Interval graduated tables besides have a equidistant step. However. the duplicating rule interruptions down in this graduated table. A temperature of 50 grades Celsius is non “half every bit hot” as a temperature of 100. but a difference of 10 grades indicates the same difference in temperature anyplace along the graduated table. The Kelvin temperature graduated table. nevertheless. constitutes a ratio graduated table because on the Kelvin graduated table nothing indicates absolute nothing in temperature. the complete absence of heat. So one can state. for illustration. that 200 grades Kelvin is twice every bit hot as 100 grades Kelvin. The differences between qualitative and quantitative informations:
Quantitative informations is informations that is associating to. mensurating. or measured by the measure of something. instead than its quality. ex: the figure of people in a town Qualitative information is informations that can be captured that is non numerical in nature ex: the colour of people’s tegument. Therefore. basically the differentiation is that quantitative informations trades with Numberss and numerical values of what is being tested. where as qualitative informations trades with the quality of what is being tested.
Qualitative data’s description can non be describe in Numberss. Quantitative data’s description can merely be described in Numberss. Cross-sectional informations. or a transverse subdivision of a survey population. in statistics and econometrics is a type of unidimensional informations set. Cross-sectional information refers to informations collected by detecting many topics ( such as persons. houses or countries/regions ) at the same point of clip. or without respect to differences in clip. Analysis of cross-sectional informations normally consists of comparing the differences among the topics. For illustration. we want to mensurate current fleshiness degrees in a population. We could pull a sample of 1. 000 people indiscriminately from that population ( besides known as a cross subdivision of that population ) . mensurate their weight and tallness. and cipher what per centum of that sample is categorized as corpulent. For illustration. 30 % of our sample were categorized as corpulent.
This cross-sectional sample provides us with a snapshot of that population. at that one point in clip. Note that we do non cognize based on one cross-sectional sample if fleshiness is increasing or diminishing ; we can merely depict the current proportion. Cross-sectional informations differs from clip series informations besides known as longitudinal informations. which follows one subject’s alterations over the class of clip. Another discrepancy. panel informations ( or time-series cross-sectional ( TSCS ) information ) . combines both and looks at multiple topics and how they change over the class of clip. Panel analysis uses panel informations to analyze alterations in variables over clip and differences in variables between topics. In a rolled cross-section. both the presence of an person in the sample and the clip at which the person is included in the sample are determined indiscriminately. For illustration. a political canvass may make up one’s mind to interview 100. 000 persons. It first selects these persons indiscriminately from the full population. It so assigns a random day of the month to each person. This is the random day of the month on which that person will be interviewed. and therefore included in the study. [ 1 ]
A clip series is a sequence of observations which are ordered in clip ( or infinite ) . If observations are made on some phenomenon throughout clip. it is most reasonable to expose the information in the order in which they arose. peculiarly since consecutive observations will likely be dependent. Time series are best displayed in a spread secret plan. The series value X is plotted on the perpendicular axis and clip T on the horizontal axis. Time is called the independent variable ( in this instance nevertheless. something over which you have small control ) . There are two sorts of clip series informations: Continuous. where we have an observation at every blink of an eye of clip. e. g. prevarication sensors. EKGs. We denote this utilizing observation Ten at clip t. X ( T ) . Discrete. where we have an observation at ( normally on a regular basis ) spaced intervals. We denote this as Xt. Examples Economics – hebdomadal portion monetary values. monthly net incomes Meteorology – daily rainfall. weave velocity. temperature Sociology – offense figures ( figure of apprehensions. etc ) . employment figures
In statistics. signal processing. pattern acknowledgment. econometrics. mathematical finance. Weather prediction. Earthquake anticipation. Electroencephalography. Control technology and Communications technology a clip series is a sequence of informations points. measured typically at consecutive clip blink of an eyes spaced at unvarying clip intervals. Examples of clip series are the day-to-day shutting value of the Dow Jones index or the one-year flow volume of the Nile River at Aswan. Time series analysis comprises methods for analysing clip series informations in order to pull out meaningful statistics and other features of the information. Time series prediction is the usage of a theoretical account to foretell hereafter values based on antecedently observed values. Time series are really often plotted via line charts. Time series informations have a natural temporal ordination. This makes clip series analysis distinct from other common informations analysis jobs. in which there is no natural ordination of the observations ( e. g. explicating people’s rewards by mention to their several instruction degrees. where the individuals’ informations could be entered in any order ) .
Time series analysis is besides distinguishable from spacial informations analysis where the observations typically relate to geographical locations ( e. g. accounting for house monetary values by the location every bit good as the intrinsic features of the houses ) . Astochastic theoretical account for a clip series will by and large reflect the fact that observations near together in clip will be more closely related than observations farther apart. In add-on. clip series theoretical accounts will frequently do usage of the natural one-way ordination of clip so that values for a given period will be expressed as derivation in some manner from past values. instead than from future values ( see clip reversibility. ) Methods for clip series analyses may be divided into two categories: frequency-domain methods and time-domain methods.
The former include spectral analysis and late wavelet analysis ; the latter include auto-correlation and cross-correlation analysis. Additionally clip series analysis techniques may be divided into parametric and non-parametric methods. The parametric attacks assume that the implicit in stationary Stochastic processhas a certain construction which can be described utilizing a little figure of parametric quantities ( for illustration. utilizing an autoregressive or moving mean theoretical account ) . In these attacks. the undertaking is to gauge the parametric quantities of the theoretical account that describes the stochastic procedure. By contrast. non-parametric attacks explicitly estimate the covariance or the spectrum of the procedure without presuming that the procedure has any peculiar construction. Additionally methods of clip series analysis may be divided into additive and non-linear. univariate and multivariate. Time series analysis can be applied to:
real-valued. uninterrupted informations
distinct numeral informations
distinct symbolic informations ( i. e. sequences of characters. such as letters and words in English linguistic communication [ 1 ] ) .
Raw informations would be the basic Numberss and inside informations collected from research without any uses. I. E. It is the “input” for any statistical computations. However. with justification. certain anomalousnesss can be removed from a information set before executing computations. or topics might be excluded if they do non run into certain predefined standards.
Categorizations of dataA. Harmonizing to Nature1. Quantitative data- information obtained from numerical variables ( e. g. age. measures. etc ) 2. Qualitative Data- information obtained from variables in the signifier of classs. features names or labels or alphameric variables ( e. g. birthdays. gender etc. ) B. Harmonizing to Source1. Primary data- first- manus information ( e. g. autobiography. fiscal statement ) 2. Secondary data- second-hand information ( e. g. life. weather prognosis from intelligence documents ) C. Harmonizing to Measurement1. Discrete data- denumerable numerical observation. -Whole Numberss merely – has an equal whole figure interval – obtained through numeration ( e. g. corporate stocks. etc. ) 2. Continuous data-measurable observations. -decimals or fractions -obtained through measurement ( e. g. bank sedimentations. volume of liquid etc. ) D. Harmonizing to Arrangement1. Ungrouped data- natural informations – no specific agreement 2. Grouped Data – organized set of informations – at least 2 groups involved -arranged Dichotomous informations are informations from results that can be divided into two classs ( e. g. dead or alive. pregnant or non pregnant ) . where each participant must be in one or other class. and can non be in both.
Your inquiry is really general. I will give you some suggestions and possibly you can paraphrase your inquiry to a specific job. I believe the inquiry can be rephrased to how a statistician may near obtaining valid informations for the intents of reading. Generally. information is collected with the intent of doing illations to a larger population which can non be surveyed. So. in statistics. the key to roll uping informations is that it is representative of the larger population that you are interested in. The statistician has picks to do in a planned observational or experimental survey. The simple random choice may be appropriate in many instances. for illustration. in a quality control state of affairs. where a sample of parts from a larger batch of parts are selected and tested. More complex sampling strategies are possible. still with the purpose that the informations can supply a important. meaningful apprehension of the population.
The agencies to cut down prejudices in these studies is really of import. Datas can be complicated. and may non state the full narrative. For case. let’s say that one route has a high figure of accidents. Is it a job of the route status. the drivers that use that route. hapless marks. excessively many issues. etc. In this illustration. statistics and other information can assist indicate to the most of import factors. It should be noted that studies are non the lone manner of roll uping informations. In instruction. informations may be in the signifier of trials tonss. GPA. etc. In media research. content analysis is often used to number and/or categorise indiscriminately sampled media content ( for illustration. comparing the volume or tone of war coverage in newspapers to telecasting ) . The list of options to study research is extended. but in all instances. the rules of random sampling and statistical premises still use. Central tendencyIn statistics. the term cardinal inclination relates to the manner in which quantitative informations tend to constellate around some value. [ 1 ]
A step of cardinal inclination is any of a figure of ways of stipulating this “central value” . In practical statistical analysis. the footings are frequently used before one has chosen even a preliminary signifier of analysis: therefore an initial aim might be to “choose an appropriate step of cardinal tendency” . In the simplest instances. the step of cardinal inclination is an norm of a set of measurings. the word norm being diversely construed as mean. average. or other step of location. depending on the context. However. the term is applied to multidimensional informations every bit good as to univariate informations and in state of affairss where a transmutation of the informations values for some or all dimensions would normally be considered necessary: in the latter instances. the impression of a “central location” is retained in change overing an “average” computed for the transformed informations back to the original units. In add-on. there are several different sorts of computations for cardinal inclination. where the sort of computation depends on the type of informations ( degree of measuring ) . Both “central tendency” and “measure of cardinal tendency” apply to either statistical populations or to samples from a population.
The followers may be applied to single dimensions of multidimensional informations. after transmutation. although some of these involve their ain inexplicit transmutation of the information. Arithmetical mean – the amount of all measurings divided by the figure of observations in the information set Median – the in-between value that separates the higher half from the lower half of the information set Mode – the most frequent value in the information set
Geometric mean – the n-th root of the merchandise of the information values Harmonic mean – the reciprocal of the arithmetic mean of the reciprocals of the information values Weighted average – an arithmetic mean that incorporates burdening to certain informations elements Distance-weighted calculator – the step uses burdening coefficients for eleven that are computed as the reverse mean distance between eleven and the other information points. Truncated average – the arithmetic mean of informations values after a certain figure or proportion of the highest and lowest information values have been discarded. Midrange – the arithmetic mean of the upper limit and minimal values of a information set. Midhinge – the arithmetic mean of the two quartiles.
Trimean – the leaden arithmetic mean of the average and two quartiles. Winsorized average – an arithmetic mean in which extreme values are replaced by values closer to the median. IntroductionA step of cardinal inclination is a individual value that attempts to depict a set of informations by placing the cardinal place within that set of informations. As such. steps of cardinal inclination are sometimes called steps of cardinal location. They are besides classed as drumhead statistics. The mean ( frequently called the norm ) is most likely the step of cardinal inclination that you are most familiar with. but there are others. such as. the average and the manner.
The mean. average and manners are all valid steps of cardinal inclination but. under different conditions. some steps of cardinal inclination go more appropriate to utilize than others. In the undermentioned subdivisions we will look at the mean. manner and average and larn how to cipher them and under what conditions they are most appropriate to be used. Mean ( Arithmetic ) The mean ( or norm ) is the most popular and good known step of cardinal inclination. It can be used with both distinct and uninterrupted informations. although its usage is most frequently with uninterrupted informations ( see our Types of Variable usher for informations types ) . The mean is equal to the amount of all the values in the information set divided by the figure of values in the information set. So. if we have n values in a information set and they have values x1. x2. … . xn. so the sample mean. normally denoted by ( marked x saloon ) . is:
This expression is normally written in a somewhat different mode utilizing the Grecian capitol missive. . marked “sigma” . which means “sum of…” :
You may hold noticed that the above expression refers to the sample mean. So. why call have we called it a sample mean? This is because. in statistics. samples and populations have really different significances and these differences are really of import. even if. in the instance of the mean. they are calculated in the same manner. To admit that we are ciphering the population mean and non the sample mean. we use the Greek lower instance missive “mu” . denoted as µ :
The mean is basically a theoretical account of your informations set. It is the value that is most common. You will detect. nevertheless. that the mean is non frequently one of the existent values that you have observed in your informations set. However. one of its of import belongingss is that it minimises mistake in the anticipation of any one value in your informations set. That is. it is the value that produces the lowest sum of mistake from all other values in the information set. An of import belongings of the mean is that it includes every value in your informations set as portion of the computation. In add-on. the mean is the lone step of cardinal inclination where the amount of the divergences of each value from the mean is ever nothing. When non to utilize the mean
The mean has one chief disadvantage: it is peculiarly susceptible to the influence of outliers. These are values that are unusual compared to the remainder of the informations set by being particularly little or big in numerical value. For illustration. see the rewards of staff at a mill below: Staff | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Salary | 15k | 18k | 16k | 14k | 15k | 15k | 12k | 17k | 90k | 95k | The average wage for these 10 staff is $ 30. 7k. However. inspecting the natural information suggests that this average value might non be the best manner to accurately reflect the typical wage of a worker. as most workers have wages in the $ 12k to 18k scope. The mean is being skewed by the two big wages.
Therefore. in this state of affairs we would wish to hold a better step of cardinal inclination. As we will happen out subsequently. taking the median would be a better step of cardinal inclination in this state of affairs. Another clip when we normally prefer the median over the mean ( or manner ) is when our informations is skewed ( i. e. the frequence distribution for our informations is skewed ) . If we consider the normal distribution – as this is the most often assessed in statistics – when the information is absolutely normal so the mean. average and manner are indistinguishable. Furthermore. they all represent the most typical value in the information set. However. as the information becomes skewed the average loses its ability to supply the best cardinal location for the information as the skewed information is dragging it off from the typical value. However. the average best retains this place and is non as strongly influenced by the skewed values. This is explained in more item in the skewed distribution subdivision subsequently in this usher. MedianThe median is the in-between mark for a set of informations that has been arranged in order of magnitude.
The median is less affected by outliers and skewed informations. In order to cipher the median. suppose we have the informations below: 65 | 55 | 89 | 56 | 35 | 14 | 56 | 55 | 87 | 45 | 92 | We foremost need to rearrange that information into order of magnitude ( smallest foremost ) : 14 | 35 | 45 | 55 | 55 | 56 | 56 | 65 | 87 | 89 | 92 | Our average grade is the in-between grade – in this instance 56 ( highlighted in bold ) . It is the in-between grade because there are 5 tonss before it and 5 tonss after it. This works all right when you have an uneven figure of tonss but what happens when you have an even figure of tonss? What if you had merely 10 tonss? Well. you merely hold to take the in-between two tonss and average the consequence. So. if we look at the illustration below: 65 | 55 | 89 | 56 | 35 | 14 | 56 | 55 | 87 | 45 | We once more rearrange that informations into order of magnitude ( smallest foremost ) : 14 | 35 | 45 | 55 | 55 | 56 | 56 | 65 | 87 | 89 | 92 | Merely now we have to take the 5th and 6th mark in our informations set and average them to acquire a median of 55. 5. ModeThe manner is the most frequent mark in our informations set. On a histogram it represents the highest saloon in a saloon chart or histogram. You can. therefore. sometimes see the manner as being the most popular option. An illustration of a manner is presented below:
Normally. the manner is used for categorical informations where we wish to cognize which is the most common class as illustrated below: Summary of when to utilize the mean. average and modePlease use the undermentioned drumhead tabular array to cognize what the best step of cardinal inclination is with regard to the different types of variable. Type of Variable | Best step of cardinal inclination | Nominal | Mode |
Ordinal | Median |
Interval/Ratio ( non skewed ) | Mean |
Interval/Ratio ( skewed ) | Median |
Measures of cardinal inclination and scattering provide a convenient manner to depict and compare sets of informations.
Importance of Statistics in Different William claude dukenfields
Statisticss plays a critical function in every Fieldss of human activity. Statistics has of import function in finding the bing place of per capita income. unemployment. population growing rate. lodging. schooling medical installations etc…in a state. Now statistics holds a cardinal place in about every field like Industry. Commerce. Trade. Physics. Chemistry. Economics. Mathematics. Biology. Botany. Psychology. Astronomy etc… . so application of statistics is really broad. Now we discuss some of import Fieldss in which statistics is normally applied. |
1 ) Business: Statisticss play an of import function in concern. A successful man of affairs must be really speedy and accurate in determination devising. He knows that what his clients wants. he should hence. cognize what to bring forth and sell and in what measures. Statistics helps businessman to be after production harmonizing to the gustatory sensation of the costumiers. the quality of the merchandises can besides be checked more expeditiously by utilizing statistical methods. So all the activities of the man of affairs based on statistical information. He can do right determination about the location of concern. selling of the merchandises. fiscal resources etc… ( 2 ) In Economicss: Statisticss play an of import function in economic sciences. Economicss mostly depends upon statistics. National income histories are multipurpose indexs for the economic experts and decision makers. Statistical methods are used for readying of these histories.
In economic sciences research statistical methods are used for roll uping and analysis the informations and proving hypothesis. The relationship between supply and demands is surveies by statistical methods. the imports and exports. the rising prices rate. the per capita income are the jobs which require good cognition of statistics. ( 3 ) In Mathematicss: Statistical plays a cardinal function in about all natural and societal scientific disciplines. The methods of natural scientific disciplines are most dependable but decisions draw from them are merely likely. because they are based on uncomplete grounds. Statistical helps in depicting these measurings more exactly. Statistics is subdivision of applied mathematics. The big figure of statistical methods like chance norms. scatterings. appraisal etc… is used in mathematics and different techniques of pure mathematics like integrating. distinction and algebra are used in statistics.
( 4 ) In Banking: Statisticss play an of import function in banking. The Bankss make usage of statistics for a figure of intents. The Bankss work on the rule that all the people who deposit their money with the Bankss do non retreat it at the same clip. The bank earns net incomes out of these sedimentations by imparting to others on involvement. The bankers use statistical attacks based on chance to gauge the Numberss of depositors and their claims for a certain twenty-four hours. ( 5 ) In State Management ( Administration ) : Statistics is indispensable for a state. Different policies of the authorities are based on statistics. Statistical informations are now widely used in taking all administrative determinations. Suppose if the authorities wants to revise the wage graduated tables of employees in position of an addition in the life cost. statistical methods will be used to find the rise in the cost of life.
Preparation of federal and provincial authorities budgets chiefly depends upon statistics because it helps in gauging the expected outgos and gross from different beginnings. So statistics are the eyes of disposal of the province. ( 6 ) In Accounting and Auditing: Accounting is impossible without exactitude. But for determination devising intent. so much preciseness is non indispensable the determination may be taken on the footing of estimate. cognize as statistics. The rectification of the values of current asserts is made on the footing of the buying power of money or the current value of it. In scrutinizing trying techniques are normally used. An hearer determines the sample size of the book to be audited on the footing of mistake. ( 7 ) In Natural and Social Sciences: Statistics plays a critical function in about all the natural and societal scientific disciplines. Statistical methods are normally used for analysing the experiments consequences. proving their significance in Biology. Physics. Chemistry. Mathematics. Meteorology. Research Chamberss of commercialism. Sociology. Business. Public Administration. Communication and Information Technology etc…
( 8 ) In Astronomy: Astronomy is one of the oldest subdivision of statistical survey. it deals with the measuring of distance. sizes. multitudes and densenesss of celestial organic structures by agencies of observations. During these measurings mistakes are ineluctable so most likely measurings are founded by utilizing statistical methods. Example: This distance of Moon from the Earth is measured. Since old yearss the uranologists have been statistical methods like method of least squares for happening the motions of stars. Collection of Statistical Data
Statistical Datas: A sequence of observation. made on a set of objects included in the sample drawn from population is known as statistical informations. ( 1 ) Ungrouped Datas: Data which have been arranged in a systematic order are called natural informations or ungrouped informations. ( 2 ) Grouped Datas: Data presented in the signifier of frequence distribution is called sorted informations. Collection of Datas: The first measure in any question ( probe ) is aggregation of informations. The information may be collected for the whole population or for a sample merely. It is largely collected on sample footing. Collection of informations is really hard occupation. The census taker or research worker is the good trained individual who collects the statistical information. The respondents ( information ) are the individuals whom the information is collected. Types of Datas: There are two types ( beginnings ) for the aggregation of informations. ( 1 ) Primary Data ( 2 ) Secondary Data |
( 1 ) Primary Data: The primary informations are the first manus information collected. compiled and published by organisation for some intent. They are most original informations in character and have non undergone any kind of statistical intervention. Example: Population nose count studies are primary informations because these are collected. complied and published by the population nose count organisation. ( 2 ) Secondary Data: The secondary informations are the 2nd manus information which are already collected by some one ( organisation ) for some intent and are available for the present survey. The secondary informations are non pure in character and have undergone some intervention at least one time. Example: Economics study of England is secondary informations because these are collected by more than one organisation like Bureau of statistics. Board of Revenue. the Banks etc… Methods of Roll uping Primary Data: Primary informations are collected by the undermentioned methods: Personal Probe: The research worker conducts the study him/herself and collects informations from it.
The information collected in this manner is normally accurate and dependable. This method of roll uping informations is merely applicable in instance of little research undertakings. Through Probe: Trained research workers are employed to roll up the information. These research workers contact the persons and fill in questionnaire after inquiring the needed information. Most of the forming implied this method. Collection through Questionnaire: The research workers get the information from local representation or agents that are based upon their ain experience. This method is speedy but gives merely unsmooth estimation. Through Telephone: The research workers get information through telephone this method is speedy and give accurate information.
Methods of Roll uping Secondary Datas: The secondary informations are collected by the undermentioned beginnings: Official: e. g. The publications of the Statistical Division. Ministry of Finance. the Federal Bureaus of Statistics. Ministries of Food. Agriculture. Industry. Labor etc… Semi-Official: e. g. State Bank. Railway Board. Central Cotton Committee. Boards of Economic Enquiry etc… Publication of Trade Associations. Chambers of Commerce etc… Technical and Trade Journals and Newspapers.
Research Organizations such as Universities and other establishments.
Difference between Primary and Secondary Data: The difference between primary and secondary information is merely a alteration of manus. The primary informations are the first manus informations information which is straight collected signifier one beginning. They are most original informations in character and have non undergone any kind of statistical intervention while the secondary informations are obtained from some other beginnings or bureaus. They are non pure in character and have undergone some intervention at least one time. For Example: Suppose we interested to happen the mean age of MS pupils. We collect the age’s informations by two methods ; either by straight roll uping from each pupil himself personally or acquiring their ages from the university record. The informations collected by the direct personal probe is called primary informations and the informations obtained from the university record is called secondary informations. Editing of Datas: After roll uping the information either from primary or secondary beginning. the following measure is its redaction. Editing means the scrutiny of collected informations to detect any mistake and error before showing it. It has to be decided before manus what grade of truth is wanted and what extent of mistakes can be tolerated in the enquiry. The redaction of secondary informations is simpler than that of primary informations.