For effective statistical analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
Data measured using the interval scale are similar to ordinal level data because they have a definite arrangement. However, in the interval level of measurement, the differences between data values are meaningful even though the data does not have a starting point.
Temperature is measured using the interval scale. It is measurable data, and the difference between...

The arithmetic mean is usually skewed towards the larger values in the data set. Therefore, to avoid this inherent bias towards smaller values, the harmonic mean is used.
Take the example of the speed of a car, which is the measure of the rate of distance traveled. If the vehicle traverses the same distance back-and-forth, its average speed equals the total distance traveled divided by the total time taken. However, if the car moves with varying speeds, then the arithmetic mean is more skewed...

When we take repeated measurements on the same or replicated samples, we will observe inconsistencies in the magnitude. These inconsistencies are called errors. To categorize and characterize these results and their errors, the researcher can use statistical analysis to determine the quality of the measurements and/or suitability of the methods.
One of the most commonly used statistical quantifiers is the mean, which is the ratio between the sum of the numerical values of all results and the...

A somewhat easy to compute quantitative estimate of a data set’s central tendency is its midrange, which is defined as the mean of the minimum and maximum values of an ordered data set.
Simply put, the midrange is half of the data set’s range. Similar to the mean, the midrange is sensitive to the extreme values and hence the prospective outliers. However, unlike the mean, the midrange is not sensitive to all the values of the data set that lie in the middle. Thus, it is prone to...

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...

Quartiles are numbers that separate the data into quarters. Quartiles may or may not be part of the data. To find the quartiles, first, find the median or second quartile. The first quartile, Q1, is the middle value of the lower half of the data, and the third quartile, Q3, is the middle value, or median, of the upper half of the data. To get the idea, consider the same data set:
1; 1; 2; 2; 4; 6; 6.8; 7.2; 8; 8.3; 9; 10; 10; 11.5
The median or second quartile is seven. The lower half of the...