The class mark is also known as the midpoint . It is the value that is in the center of a class and represents all the values that are in a certain category. Fundamentally, it is used to calculate various parameters , such as the arithmetic mean or the standard deviation . Class mark in statistics
The value of the class mark is also very useful to be able to find the variant of a set of a series of data that are already grouped by class and at the same time it allows us to understand the distance that these certain data have from the center.
What is a class mark for?
As mentioned previously, the class mark has a great functionality to reach the arithmetic mean and the variance of a certain group of data that in turn have already been grouped into different classes.
The arithmetic mean can be defined as the sum of all those observations obtained from the sample size. If viewed from the physical point of view, it can be interpreted as the break-even point of a group of data. Class mark in statistics
The data mark is used to fully identify a data set , but it could be very risky, therefore the difference between the breakeven point and the actual data must be taken into account. These values are known as the derivation of the arithmetic mean and, in turn, seek to determine how the arithmetic mean of the data can vary.
The most common way that this value can be found is through the variance. This variance is the average of the squares of the deviations from the arithmetic mean. To perform the calculation of both the variance and the arithmetic mean of a group of data found in a class, some referenced formulas must be used.
Calculate a class mark
As previously stated, the class mark is known as the midpoint of each interval . It is the value that represents the interval as a whole to perform the calculations of certain parameters such as the standard deviation.
In order to calculate it, the following steps must be followed:
- The class mark (Xi) is calculated, which is the average of each interval or the mean value. This serves to make it much easier to calculate the different position and dispersion measurements.
- When the number of intervals has been chosen, the amplitude of each class or interval (C) can be determined. Class mark in statistics
- This amplitude must be equal to the range of the data that is divided into the number of intervals.
- In the first interval, the lowest data value must be contained and conversely the last interval must have the highest data value.
- You must determine the number of intervals or class (K) that are used to be able to perform the grouping of the data.
- The most appropriate is to have between 5 and 20 intervals or classes (K).
- Despite this, if there is no certainty of the number of intervals to be used, the rule called Sturges Rule can be applied. With it, it is possible to have a fairly accurate approximation of the number of intervals that are needed to group them.
- This Sturges Rule allows the calculation of the class quantity to be carried out, once the size of the population or sample is known.
What is a class mark for grouped data like?
Within a table of data grouped by intervals, the real values taken by the variable may be unknown . To calculate the measures of centralization, it must be considered that the values are uniformly distributed in the intervals. Class mark in statistics
This can also happen if similar data is grouped in intervals. When this is done, you run the risk of forgetting your true values and only your approximations that the uniform interval distribution assumes are considered.
All of this can lead to variations in centralized measurements, once data that is known to be ungrouped or grouped by intervals is considered, which means it will not be large.
If the sample contains between 30 or more data, it is advisable to group the data by class classification, then the characteristics of the sample should be determined and then those of the population from which it was taken.
To group the data, the following steps must be followed:
Determine the range or path of the data
Range = Higher value – Lower value
Set the number of classes (K)
In order to establish the number of classes where the data will be grouped, it is necessary to have a base such as the ones that can be seen in the following table. Class mark in statistics
Sample size or number of data
Number of classes
|Less than 50||From 5 to 7|
|From 50 to 99||From 6 to 10|
|From 100 to 250||7 to 12|
|More than 250||10 to 20|