Chapter 5: Descriptive Statistics PDF

University of Blida 1 first year LMD (NLS) Faculty of Natural and Life sciences 2023/2024 Module: Maths-Statistics Mr. BAYASLI Chapter 5 : Descriptive statistics 1.Introduction : Statis...

University of Blida 1 first year LMD (NLS) Faculty of Natural and Life sciences 2023/2024 Module: Maths-Statistics Mr. BAYASLI Chapter 5 : Descriptive statistics 1.Introduction : Statistics is a scientific method which consists of gathering numerical data on numerous sets, then analyzing, commenting on and criticizing this data. The first properly compiled statistics were those from demographic censuses. Thus the statistical vocabulary is essentially that of demography. The groups studied are called populations. The elements of the population are called individuals or statistical units. The population is studied according to one or more characteristics. Descriptive statistics can be summarized by the following diagram: POPULATION SAMPLE Characteristic of g the Sample SAMPLING Deduction Radom 2. Statistical observation method: To collect information on a statistical population, there are two methods:  the exhaustive method or census where each individual in the population is studied according to the character(s) studied.  the method of surveys or sampling which leads to examining only a fraction of the population, a sample. 3. Vocabulary used in statistics: 3-1 Statistical population: this is the set of all individuals in whom the statistical study is interested. Example :  Students from the Biology Faculty.  Faculty of Biology car park. 3-2 Statistical unit or (individual): a element of this set or more, precisely the element which makes up the population. 1 3-3 The sample: it is a part or a subset of the parent population. Example : L1 students from the biology faculty. 3-4 Static character: this is the property retained to develop the statistical study. Example : age, height, weight, level of interaction. 3-5 Modality: modalities are different possible states of a character. Example : Character: Sex of students Modality: feminine or masculine A character can be qualitative or quantitative: Qualitative: when it cannot be expressed in volume, it cannot be measured or qualified; but only spotted it. Example: car color Quantitative: when it can be expressed in value, it is measurable and quantifiable Example: the number of children of a couple. A quantitative character can be (discrete or continuous): Discrete: if the modalities are whole numbers, isolated. Example: number of rooms in a home. Continue: if the modelers are expressed in value intervals. Example: weight, height. (poids, taille) A qualitative character can be (nominal or ordinal): Nominal: if the modalities can be expressed by nouns. Example: blood groups, different DNA nucleotides. Ordinal: if the modalities reflect the degree of a state characterizing an individual without this degree being able to be defined by a number resulting from a measurement. Example: mention of an exam. 3-6 Class: it is a grouping of values according to intervals which may or may not be equal, a class redefines two limits, the lower limit and the upper limit. 3-7 The absolute number or frequency: this is the number of individuals having a value of the modality Example: 18 women, 12 men 3-8 Relative frequency: this is the share of the modality’s effective in the total effective. Example : F1 = 18/30 ; F2 = 12/30 3-9 Statistical series: this is the set of values that measure character. 2 4. Data representation: 4-1 Statistical series: A statistical series corresponds to the different modalities of a character on a sample of individuals belonging to a given population. The number of individuals who constitute the sample studied is called the sample size. Example : In order to study the population structure of ruffed grouse (Bonasa umbellus) killed by Canadian hunters, a study of the sexual dimorphism of this species was undertaken. Among the traits measured is the length of the central rectrice (tail feather). The observed results expressed in millimeters on a sample of 50 juvenile males are noted in the series above: 4-2 Statistical tables: The frequency distribution table is a synthetic way of presenting data. Its constitution is immediate in the case of a discrete character but on the other hand requires a transformation of the data in the case of a continuous character. 4-2-1 Absolute, relative and cumulative frequencies: To each modality of the character , one or more individuals in the sample of size can correspond. We call the effective of the modality , the number where is the number of individuals. We call the frequency of the modality , the number such that We call cumulative frequencies or cumulative relative frequencies in , the number cum such that: ∑ 4-2-2 Discrete quantitative characteristics In the case of a discrete quantitative character, the establishment of the distribution of observed data associated with their frequencies is immediate. Example : 3  The sample size studied is n =375 sheets 4-2-3 Continuous quantitative characteristics In the case of a continuous quantitative nature, the establishment of the frequency table involves first carrying out a distribution into classes of the data. This requires defining the expected number of classes and therefore the amplitude associated with each class or class interval. As a general rule, we choose classes of the same amplitude. For the frequency distribution to be meaningful, each class must include a sufficient number of values (ni). Various empirical formulas make it possible to establish the number of classes for a sample of size n. In the case of a continuous quantitative nature, the establishment of the frequency table involves first carrying out a distribution into classes of the data. This requires defining the expected number of classes and therefore the amplitude associated with each class or class interval. As a general rule, we choose classes of the same amplitude. For the frequency distribution to be meaningful, each class must include a sufficient number of values. Various empirical formulas make it possible to establish the number of classes for a sample of size. STURGE'S RULE : Numbre of classes = 1+ (3,3 log N) YULE's rule : Numbre of classes = 2,5 √ 4 The interval between each class is then obtained as follows: with and , respectively the largest and smallest value of in the statistical series. From we obtain the class limits or class limits by successive addition of the class interval. As a general rule, we try to make the class index or central value of the class coincide with a whole number or one with few decimal places. 5