We begin with a an easy example. There are millions of passenger automobiles in the unified States. What is their median value? that is clearly impractical to effort to solve this trouble directly by assessing the worth of every solitary car in the country, add up all those values, then divide by the number of values, one for each car. In practice the best we deserve to do would certainly be to estimate the typical value. A natural way to perform so would be to randomly select some that the cars, to speak \(200\) that them, ascertain the worth of every of those cars, and also find the average of those \(200\) values. The collection of all those countless vehicles is dubbed the population of interest, and also the number fastened to each one, that value, is a measurement. The typical value is a parameter: a number that explains a characteristics of the population, in this situation monetary worth. The collection of \(200\) car selected from the population is referred to as a sample, and also the \(200\) numbers, the monetary values that the cars we selected, are the sample data. The average of the data is dubbed a statistic: a number calculated native the sample data. This instance illustrates the meaning of the complying with definitions.
You are watching: The branch of statistics that involves organizing, displaying, and describing data.
Definitions: populations and also samples
A population is any details collection that objects the interest. A sample is any type of subset or subcollection that the population, consisting of the instance that the sample is composed of the totality population, in which instance it is termed a census.
Definitions: measurements and Sample Data
A measurement is a number or attribute computed because that each member that a populace or that a sample. The dimensions of sample elements are collectively called the sample data.
A parameter is a number the summarizes some facet of the population as a whole. A statistic is a number computed from the sample data.
Continuing through our example, if the typical value of the cars in our sample to be \($8,357\), climate it seems reasonable come conclude that the typical value of all cars is about \($8,357\). In reasoning this way we have drawn an inference about the population based upon information derived from the sample. In general, statistics is a examine of data: describing properties of the data, which is dubbed descriptive statistics, and also drawing conclusions around a populace of attention from information extracted indigenous a sample, which is referred to as inferential statistics. Computing the solitary number \($8,357\) to summarize the data was an procedure of descriptive statistics; making use of it to do a statement around the populace was an operation of inferential statistics.
Statistics is a repertoire of methods for collecting, displaying, analyzing, and drawing conclusions from data.
Definition: Descriptive statistics
Descriptive statistics is the branch that statistics that involves organizing, displaying, and describing data.
Definition: Inferential statistics
Inferential statistics is the branch that statistics that involves drawing conclusions about a populace based on information had in a sample taken from the population.
The measurement make on each element of a sample need not it is in numerical. In the instance of automobiles, what is provided about each car could be its color, the make, its human body type, and also so on. Such data space categorical or qualitative, together opposed to numerical or quantitative data together as value or age. This is a general distinction.
Definition: Qualitative data
Qualitative data are measurements for which there is no organic numerical scale, however which covers attributes, labels, or various other non-numerical characteristics.
Definition: Quantitative data
Quantitative data are numerical measurements that arise from a organic numerical scale.
Qualitative data deserve to generate numerical sample statistics. In the vehicle example, because that instance, we might be interested in the relationship of all cars that are much less than 6 years old. In our exact same sample the \(200\) car we might note because that each automobile whether it is much less than six years old or not, i m sorry is a qualitative measurement. If \(172\) dare in the sample are much less than six years old, i beg your pardon is \(0.86\) or \(86\% \), then we would certainly estimate the parameter the interest, the population proportion, come be about the same as the sample statistic, the sample proportion, that is, around \(0.86\).
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The relationship between a populace of interest and also a sample drawn from that population is probably the most important principle in statistics, because everything rather rests top top it. This partnership is depicted graphically in number \(\PageIndex1\). The circles in the big box represent aspects of the population. In the number there to be room for just a small variety of them however in really situations, favor our auto example, lock could very well number in the millions. The solid black color circles represent the elements of the populace that space selected in ~ random and that together type the sample. Because that each element of the sample over there is a measure of interest, denoted by a lower case \(x\) (which we have actually indexed together \(x_1 , \ldots, x_n\) come tell them apart); these dimensions collectively type the sample data set. From the data we might calculate assorted statistics. To anticipate the notation that will certainly be supplied later, we might compute the sample typical \(\barx\) and also the sample ratio \(\hatp\), and take them as approximations come the population mean \(\mu\) (this is the lower situation Greek letter mu, the timeless symbol for this parameter) and the populace proportion \(p\), respectively. The various other symbols in the number stand for various other parameters and also statistics the we will certainly encounter.