Probabilistic sampling: It is a sample process in which the elements are chosen by random methods, that is, the selection of the elements for the sample is carried out by random procedures and with known selection probabilities.
applied-statistics-indicators-managementSAMPLING
Sample selection methods
Probabilistic sampling: It is a sample process in which the elements are chosen by random methods, that is, the selection of the elements for the sample is carried out by random procedures and with known selection probabilities.
SAMPLING
Sample selection methods
1-Simple random sampling: It is a selection of samples in which the elements or units are chosen individually and directly through a random process, in which each unselected element has the same opportunity to be chosen as all the others elements in each sample extraction. So each item in the population must have an equal probability of being selected.
SAMPLING
Sample selection methods
2-Systematic sampling: The elements are selected in an ordered way and depend on the number of elements or units included in the population and the size of the sample. Requires the use of a list of all the elements of the population.
SAMPLING
Sample selection methods
3-Stratified sampling: The population is divided into a certain number of subgroups or strata, each of which is sampled independently. The process through which the population is divided into subgroups or strata, is called stratification. The purpose of the stratification is to carry out separate selections in each of the subgroups or strata.
SAMPLING
Sample selection methods
Non-probability sampling: Includes all methods in which the sample elements are not selected by random or random procedures, or with known selection probabilities. Some selection procedures for non-probability sampling are:
- Judgment sampling: Quota sampling: decisional sampling: Causal grouping sampling:
STATISTICAL DATA
The data of quantitative characteristics: they are those that can be expressed numerically and are obtained through measurements and counts. A quantitative data can be found in any discipline; psychology, accounting, economics, advertising etc
STATISTICAL DATA
The data with quantitative and qualitative characteristics are classified in turn into:
1-Continuous variables:
2-Discrete variables:
STATISTICAL DATA
Data with qualitative characteristics: Data with qualitative characteristics are those that cannot be expressed numerically. These data must be converted to numerical values before working with them.
STATISTICAL DATA
The qualitative characteristics data are classified into:
1-Nominal data: They include categories, such as sex, study career, floor material, qualifications, etc.
2-hierarchical data: subjective evaluations when concepts are ranked according to preference or achievement
STATISTICAL DATA
Frequency distribution: When you have a large mass or quantity of data, it is sometimes very difficult to group them.
This way of organizing information is called frequency distribution and consists of the ordering of the data through classes and frequencies.
STATISTICAL DATA
When the data are presented in a frequency distribution, they are called grouped data. When all the observed data of a variable are listed in a disorganized way, we will call it ungrouped data.
DISTRIBUTION OF
FREQUENCIES
Introduction
The preliminary phase of any statistical study is based on the collection and ordering of data; This is done with the help of numerical and graphical summaries.
Position measurements
These are the measures that help us know where the data is but without indicating how it is distributed.
Steps to build a distribution of frequencies: already known all the theoretical elements necessary for the construction and understanding of a distribution of frequencies we will proceed to show the steps required for its implementation.
3 ° Calculate the number of classes, provided that the class interval is known.
NC = R
Ci
As can be seen in the second and third steps, it would be very difficult to solve these equations by simple mathematical methods since each of them presents two unknowns.
In statistics, a histogram is a graphical representation of a variable in the form of bars, where the surface of each bar is proportional to the frequency of the represented values.
It is used when studying a continuous variable, such as age ranges or sample height, and, for convenience, its values are grouped into classes, that is, continuous values. In cases where the data is qualitative (non-numerical), such as sixth grade agreement or educational level, a sector diagram is preferable.
Frequency polygon
A graph made by joining the midpoints at the top of the columns of a frequency histogram.
Bar graph
It is a set of rectangles or bars separated from each other, because it is used to represent discrete variables; the bars must be of the same base or width and separated at the same distance. They can be arranged vertically and horizontally.
Linear Graph
A line graph is used to represent data series that have been collected at a specific time. The data is plotted on a graph at time intervals and a line is drawn connecting the resulting points.
CIRCULAR GRAPH:
100% bar graph and circle graph: They are especially used to represent the parts into which a total quantity is divided.
The warhead:
The warhead: This graph consists of the representation of the accumulated frequencies of a frequency distribution. It can be built in two different ways; on the “less than” or on the “or more” basis. You can determine the median value of the distribution.
EXAMPLES TO DISCUSS
MEASURES OF ARITHMETIC AVERAGE POSITION
One of the measures that characterize a distribution is the arithmetic mean, which is obtained by adding the entered x i values, and dividing by the total number N
THE STATISTICAL MEDIUM
It is the value of the variable that leaves the same number of data before and after it, once they have been ordered. According to this definition, the data set less than or equal to the median will represent 50% of the data, and those that are greater than the median will represent the other 50% of the total sample data.
THE STATISTICAL MEDIUM
To understand this concept we are going to assume that we have the ordered series of values (2, 5, 8, 10 and 13), the position of the median would be:
THE STATISTICAL MEDIUM
And if the ordered series were (2, 5, 8, 10,13 and 15), the position of the median would be:
That is, position three and a half. Since it is impossible to highlight the three and a half position, it is necessary to average the two values of the third and fourth positions to produce an equivalent median, which in this case correspond to (8 + 10) / 2 = 9. Which would indicate that half of the values are below the value 9 and the other half is above this value.
FASHION
FASHION
The modal measure indicates the value that is most often repeated within the data; that is, if we have the ordered series (2, 2, 5 and 7), the value that is repeated most often is number 2 who would be the mode of the data. It is possible that in some occasions two values are presented with the highest frequency, which is called Bimodal or in other cases more than two values, which is known as multimodal.
Measures of central tendency
Measures of central tendency
They allow us to identify the most representative values of the data, according to the way they tend to be concentrated.
The Average indicates the average of the data; that is, it informs us of the value that each of the individuals would obtain if the values were distributed in equal parts.
Measures of central tendency
The Median, by contrast, informs us of the value that separates the data into two equal parts, each of which has fifty percent of the data.
Finally, Fashion indicates the value that is most repeated within the data
POSITION MEASURES POSITION MEASURES
Position measurements divide a data set into groups with the same number of individuals.
To calculate the position measurements it is necessary that the data are ordered from least to greatest.
POSITION MEASURES
Quartiles
The quartiles are the three values of the variable that divide an ordered data set into four equal parts.
Q1, Q2 and Q3 determine the values corresponding to 25%, 50% and 75% of the data.
Q2 coincides with the median.
POSITION MEASURES
Deciles
Deciles are the nine values that divide the data series into ten equal parts.
The deciles give the values corresponding to 10%, 20%… and 90% of the data.
D5 coincides with the median.
POSITION MEASURES
Percentiles
Percentiles are the 99 values that divide the data series into 100 equal parts.
The percentiles give the values corresponding to 1%, 2%… and 99% of the data.
P50 coincides with the median.
MEASUREMENTS
OF
DISPERSION
MEASURES OF DISPERSION
MEASURES OF DISPERSION
The range is the difference between the largest and smallest of the data in a distribution
statistics
MEASURES OF DISPERSION
The deviation from the mean is the difference between each value of the statistical variable and the arithmetic mean.
D i = x - x
MEASURES OF DISPERSION
The mean deviation is the arithmetic mean of the absolute values of the deviations from the mean
The mean deviation is represented by
MEASURES OF DISPERSION
Variance Properties
- The variance will always be a positive value or zero, in the event that scores are iguales.Si all values of the variable are added one number the variance does not change.
MEASURES OF DISPERSION
Variance Properties
3 If all the values of the variable are multiplied by a number, the variance is multiplied by the square of that number.
MEASURES OF DISPERSION
Variance Properties
4 If we have several distributions with the same mean and we know their respective variances, the total variance can be calculated.
MEASURES OF DISPERSION
Observations on variance
- The variance, equal to the average, is a very sensitive index scores extremas.En cases can not find the media it will not be possible to find the variance.
MEASURES OF DISPERSION
Observations on variance
3 The variance is not expressed in the same units as the data, since the deviations are squared.
MEASURES OF DISPERSION
Standard deviation
The standard deviation (σ) measures how far the data is separated.
The formula is easy: it is the square root of the variance. So "what is variance?"
MEASURES OF DISPERSION
Standard deviation Variance
The variance (which is the square of the standard deviation: σ 2) is defined as:
It is the mean of the squared mean differences.
MEASURES OF DISPERSION
Standard deviation
In other words, follow these steps:
Calculate the mean (the average of the numbers)
MEASURES OF DISPERSION
Standard deviation
Now, for each number, subtract the mean and square the result (the squared difference).
MEASURES OF DISPERSION
Standard deviation
Now calculate the mean of those differences squared. (Why squared?)
MEASURES OF DISPERSION
Standard deviation
(Why squared?)
Squared each difference makes all numbers positive (to prevent negative numbers from reducing variance)
MEASURES OF DISPERSION
Standard deviation
And they also make big differences stand out. For example 100 2 = 10,000 is much larger than 50 2 = 2,500.
But squaring them makes the answer very large, so we undo it (with the square root) and so the standard deviation is much more useful
MEASURES OF DISPERSION
Download the original file
