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Statistical Data Presentation (Central Trend and Dev.) - Coggle Diagram
Statistical Data Presentation (Central Trend and Dev.)
Average or Average
Average or Average
The average is an average. It is calculated by adding all the data and then dividing the total by the number of data involved.
If we have a set of data, we can calculate the mean of the set and in this way we will summarize all the information in a single number. All the data in the set are around that number or average. Instead of a table, we would be left with a single number. That makes it easier to analyze the data.
The mean acts as an equilibrium point in such a way that smaller observations compensate for larger observations.
The arithmetic mean is largely affected by extreme values.
When high school students add up all their partial grades and divide them by the number of grades, they get their partial average. That average is the arithmetic mean of your partial grades.
Median and Mode
Median
It is the mean value of an ordered sequence of data. If there are no ties, half of the observations will be lower and the other half will be higher.
The median is not affected by extreme values.
Mode
In a data series, the mode is the value that is repeated the most, the one that appears most frequently. The mode is not affected by the occurrence of any extreme value.
Range, Variance and Standard Deviation
a_Range
Although we have measures of central tendency that indicate the center of a data set, many times these measures do not show us the reality completely.
For example, suppose the average (mean) age in your classroom is 28 years. Most members may indeed be around that age, but that is not necessarily going to happen for all members. Some may be over 40, and even others under 20.
Range is the difference between the highest and the lowest observation in a data series. The range measures the total spread in the data series. The formula for the range would then be:
Formula of the range r = X - X
b_The Variance and Standard Deviation
The variance and standard deviation take into account how the observations are distributed. Sample variance is the average of the squared differences between each of the observations in a data series and the mean.
The Coefficient of Variation
The Coefficient of Variation
To compare the dispersion of variables that appear in different units (meters, kilos, etc.) or that correspond to extremely unequal populations, it is necessary to have a measure of variability that does not depend on the units or the size of the data.
This coefficient only serves to compare the dispersions of variables corresponding to ratio scales.
One way of constructing a measure of variability that meets the above requirements is called
coefficient of variation
.
CV = S / X
The measures of central tendency are those that indicate the center of a data set.