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statistics

A histogram is visual representation of a distribution of the characteristics of a sample or a population that uses bars of certain might not necessarily be equal lengths , to denote the number of the members of the population or of the sample that has the required or observed characteristics in interval form (NetMBA , www .netmba .com Unlike the bar graph , the histogram considers that area of the rectangular bar to denote the frequency of

a variable , that is , the area obtained by multiplying the length of interval and the height of the rectangular bar . For example , a rectangular bar on a histogram drawn over the interval 0 to 5 with the height of 10 has a frequency 50 , that is , there are 50 members of the sample or population with a certain characteristics with measures between 0 to 5 inclusive . Through this example , we can deduce that histograms can only be constructed from a distribution of numerical data (Simon , www .isixsigma .com

Similarly , the density curves also visually present the distribution of the characteristics of the members of the sample or the population through the use of the area . The frequency can be computed by taking the area below the curve of a density curve over an interval . The major difference between the two is that histograms consider a discrete numerical distribution while the density curves takes distributions with continuous values (srv2 .lycoming .edu .Discrete numerical values are those that takes distinct specific measures or amounts within an interval . Some discrete data are number of ice creams sold per day number of children in a family , or number of students who has passed the examination . Such variables can be numbered as 0 , 1 , 2 , 3 and so on . On the other hand , continuous numerical data are those that have infinitely many values that can be taken throughout the interval and for those reason , they cannot be discretely enumerated as the examples above . Some of continuous numerical data are height of a student , lap time for a Formula 1 racer , or depth of the sea during an instant of time (infinity .cos .edu

Such difference between discrete and continuous numerical data is one of the reasons why density curves are constructed . They had observed the limitation of the histogram in visually presenting continuous variable in a population or sample

Another reason in the rise and development of major density curves is to improve the accuracy of basic descriptive statistics method in application on inferential statistics (srv2 .lycoming .edu . Usually , in a statistical study conducted in several fields , populations are composed of millions or even billions of members . In inferential statistics samples are taken and the characteristic of concern is observed and then the data is manipulated . Due to the discrepancies , only a histogram can be prepared to give the idea of the shape of the distribution . If the whole population is to be considered , the shape of the distribution is said to be not like rectangular adjacent bars like the histogram , but a smooth curve which is the density curve (srv2 .lycoming .edu . In this way , errors in not considering other members of the population is minimized or somehow reduced to a more tolerable level which is important in doing analysis

Since the density curve is made through the modification of the histogram , some of the measures of central tendency and dispersion can be observed in the same manner as taking a look at each of the two of them . In histogram , the mean can be estimated as the number where the bars tend to be clustering . It is like a number on the tallest bar if this tallest bar has adjacent bars with almost the same height as him otherwise , the median can be found somewhere else . In general , it can be found in the point where the area of the rectangle cancels each other or where the area on the right of this point is equal to the area to the right of this point . The mode is simply found in the highest rectangular bar which is given in interval form , though there are other computations that must be made so a single value can be obtain (www .herkimershideaway .org

In stochastic studies or probability theory , density curves are visualized or interpreted as a tool that gives or presents the probability that the taken member of the population has the characteristic of concern with measure between specified intervals (www .stat .stanford .edu . This can be best illustrate if we introduce the normal curve - the distribution with the mean equal to 0 and variance equal to 1 , shaped like a bell or an inverted cursive V with two legs extending infinitely on opposite sides (www .herkimershideaway .org

The fact that the area below the standard normal curve is one makes it a powerful tool in assignment of probabilities . Recall that the range of probability values would only be defined if it is between 0 and 1 inclusive . For example , the probability that the certain variable is greater than 0 is ? if the distribution of the variable is known to be standard normal . That is because the area on the right of 0 is ? and the area on its left is also , so the probability that the variable is greater than 0 is equal to the area under the curve on the right of 0 In to solve for other probabilities that involves interval other than 0 to infinity or negative infinity , probabilistic identities must be studied . Today , there are many devices that computes fro this kind of probabilities like the computer or calculator especially when the distribution is standard normal . There are still standard normal tables and other useful distribution like the t-distribution and chi-square which is of great use to statistics

Basically , the only essential difference between histograms and density curves is the kind of data that they consider . The first one recognizes the discrete numerical data while the latter talks about or presents the continuous numerical data . Due to the power of density curves in presenting continuous data , they can be used in other problems such as probability Reference

Density Curves and Normal Distributions . Retrieved November 14 , 2007 from http /www . herkimershideaway .org /apstatistics /ymmsum99 /ymm221 .htm

Density Curves and Z-scores . Retrieved November 14 , 2007 from http /srv2 . lycoming .edu sprgene /M123 /Text /UNIT_15 .pdf

Discrete and Continuous Data . Retrieved November 14 , 2007 from http /infinity .cos .edu /faculty /woodbury /Stats /Tutorial /Data_Disc_Cont .h tm

NetMBA Business Knowledge Center . The Histogram . Retrieved November 14 2007 from http /www .netmba .com /statistics /histogram

Simon , Kerri . Histogram . Retrieved November 14 , 2007 http /www .isixsigma . com /library /content /c010527c .asp

The Normal Distribution . Retrieved November 14 , 2007 from http /www-stat .stanford .edu naras /jsm /NormalDensity /NormalDensity .html statistics PAGE \ MERGEFORMAT 1 ...