calculate the quartile deviation and its Coefficient from the following data 15, 18 ,20 21 22 ,23, 24 ,25 ,26 ,28 ,29 ,30, 32 ,33, 35
Answers
Answer:
........------.....
Step-by-step explanation:
__------""......._--.._._........____
Answer:
The Quartile Deviation is a simple way to estimate the spread of a distribution about a measure of its central tendency (usually the mean). So, it gives you an idea about the range within which the central 50% of your sample data lies. Consequently, based on the quartile deviation, the Coefficient of Quartile Deviation can be defined, which makes it easy to compare the spread of two or more different distributions. Since both of these topics are based on the concept of quartiles, we’ll first understand how to calculate the quartiles of a dataset before working with the direct formulae.
Step-by-step explanation:
Quartiles
A median divides a given dataset (which is already sorted) into two equal halves similarly, the quartiles are used to divide a given dataset into four equal halves. Therefore, logically there should be three quartiles for a given distribution, but if you think about it, the second quartile is equal to the median itself! We’ll deal with the other two quartiles in this section.
The first quartile or the lower quartile or the 25th percentile, also denoted by Q1, corresponds to the value that lies halfway between the median and the lowest value in the distribution (when it is already sorted in the ascending order). Hence, it marks the region which encloses 25% of the initial data.
Similarly, the third quartile or the upper quartile or 75th percentile, also denoted by Q3, corresponds to the value that lies halfway between the median and the highest value in the distribution (when it is already sorted in the ascending order). It, therefore, marks the region which encloses the 75% of the initial data or 25% of the end data.
JOIN NOW
Search for a topic
Business Mathematics and Statistics > Measures of Central Tendency and Dispersion > Quartiles, Quartile Deviation and Coefficient of Quartile Deviation
Measures of Central Tendency and Dispersion
Quartiles, Quartile Deviation and Coefficient of Quartile Deviation
The Quartile Deviation is a simple way to estimate the spread of a distribution about a measure of its central tendency (usually the mean). So, it gives you an idea about the range within which the central 50% of your sample data lies. Consequently, based on the quartile deviation, the Coefficient of Quartile Deviation can be defined, which makes it easy to compare the spread of two or more different distributions. Since both of these topics are based on the concept of quartiles, we’ll first understand how to calculate the quartiles of a dataset before working with the direct formulae.
Suggested Videos
ArrowArrow
ArrowArrow
Measures of Central Tendency
Quartile Deviation and Coefficient of Quartile Deviation
Measure of Dispersion
Solve
Questions
Quartiles
A median divides a given dataset (which is already sorted) into two equal halves similarly, the quartiles are used to divide a given dataset into four equal halves. Therefore, logically there should be three quartiles for a given distribution, but if you think about it, the second quartile is equal to the median itself! We’ll deal with the other two quartiles in this section.
The first quartile or the lower quartile or the 25th percentile, also denoted by Q1, corresponds to the value that lies halfway between the median and the lowest value in the distribution (when it is already sorted in the ascending order). Hence, it marks the region which encloses 25% of the initial data.
Similarly, the third quartile or the upper quartile or 75th percentile, also denoted by Q3, corresponds to the value that lies halfway between the median and the highest value in the distribution (when it is already sorted in the ascending order). It, therefore, marks the region which encloses the 75% of the initial data or 25% of the end data.
Browse more Topics under Measures Of Central Tendency And Dispersion
Arithmetic Mean
Median and Mode
Partition Values or Fractiles
Harmonic Mean and Geometric Mean
Measure of Dispersion
Range and Mean Deviation
Standard deviation and Coefficient of Variation
The Quartile Deviation doesn’t take into account the extreme points of the distribution. Thus, the dispersion or the spread of only the central 50% data is considered.
If the scale of the data is changed, the Qd also changes in the same ratio.
It is the best measure of dispersion for open-ended systems (which have open-ended extreme ranges).
Also, it is less affected by sampling fluctuations in the dataset as compared to the range (another measure of dispersion).
Since it is solely dependent on the central values in the distribution, if in any experiment, these values are abnormal or inaccurate, the result would be affected drastically.