# Elucidate the properties and limitations of quartile deviation and average deviation.

Answer – Introduction – Quartile Deviation, A measure of dispersion, which can be obtained by dividing the difference between Q3 and Q1 by two. Average Deviation, A measure of dispersion which gives an average difference between each item and mean (ignoring plus and minus sign).

## Quartile Deviation –

Since the large number of data between the frequency distribution and the range depends on the extremes of distribution, so we need another solution for variability. Quartile deviation represented by Q is a measurement, depending on the relatively stable middle part of the distribution. Quartile is defined as “half distance between the first and third quartile point”. According to geography, quadratic deviation or Q is the distinction between the 75th and 25th percentile, is a frequency distribution. According to Gilford (1963) semi-fourth grade category Q, half of the mid-50 percent cases are in the category. Based on the above definition, it can be said that quarter deviation is half of the distance between Q1 and Q3.

Q.D = (Q3 – Q1)/ 2

Where Q1 and Q3 are the first and third quartiles of data. What are Qualrtiles? Quartile is an additional way to separate the data. Each quartile represents a quarter or group of the entire population. There is an attractive feature in quartile deviation that the range “mean + Q.D” contains approximately 50% of the data. Quartile deviation is also an absolute measure of dispersion. Its relative measure is called the quartile deviation or the coefficient of the quasi-quartile range. It is defined by relation;

Coefficient of quartile deviation= (Q3 – Q1)/(Q3 + Q1)

## Properties of quartile deviation

Quadrant deviation or Q frequency distribution is half the distance between the 75th and 25th percentiles. The 25th percentile or Q1 is the first quartile on the score scale whose bottom score is 25%. The third quartile on the 75th percentile or scale of Q3 score is 75% of the numbers given below. To find Q, we must first calculate Q3 and Q1. In all cases there are grouped data and uncontrolled data and in order to calculate quartile deviation, we have to first find out whether this is a grouped data ore ungrouped data. We will first see how Q is calculated from uncontrolled data.

Quartile deviation is closely related to the median because the mean is responsible for the number of points under their exact positions, and Q1 and Q3 are defined in the same way. There are common properties in medieval and quartile deviations. Mid and quartile deviations are not influenced by both excessive values. In non-symmetrical distribution, two quarters of Q1 and Q3 are equal to the median – Q1 = Q3-Median. Thus, the medial Quartile Onion cover measures exactly 50 percent of the values ​​seen in the deviation data. If the distribution is open, then the only solution to the proper variability compared to quartile deviation is that the distribution has ended.

## limitations of quartile deviation –

1) The cost of quartile deviation is based on mid 50 percent values, it is not based on all comments. Quartile deviation ignores 50% of the items, i.e., the first 25% and the last 25%. Since the value of quartile deviation does not depend on each item of the chain, it can not be considered as a good method of measuring dispersion.

2) The value of quartile deviation is influenced by the fluctuation in the sample.
3) The value of quartet deviation is not affected by the distribution of the values ​​of the person within the interval of 50 percent observed values.

4) It is not able to manipulate mathematical

5) Its value is greatly influenced by the fluctuation model.

6) This is not really the measure of dispersion because it does not really show scatter around an average, but T is an average position. As a result, some statisticians talk of Quartet Deviation as a measurement of division rather than measure of dispersion. If we really want to measure the difference in the meaning of the scattering around the average, then we should include the deviation of each object on average, in the measurement.

## Average Deviation –

According to Garrett (1981). “Average Deviation means the deviation of all the different digits, the series taken from their Average”. According to Gilford (1963), “when we ignore the algebraic signs, then the Average deviation is the arithmetic average of all deviations”

## Properties of Average Deviation

1. Calculation of average deviation is easy because it is a popular solution.
2. When we calculate the average deviation, then the equal weight of each observed values ​​is given and thus it indicates how far each observation means.
3. When the deviation is taken from mediocrity, deviation takes its minimum value.
4. Mean deviation remains unchanged due to the original change, but due to changes in scale, it changes in the same proportion. That is, if two variables are related to x and y, y = a + bx, a and b constants, then Md of y = | b | x MD of X.

## limitations of Average Deviation –

1. The main limitation of average deviation is that while calculating the average deviation, we ignore Plus Minus sign and consider all the values ​​plus.
2. Due to this mathematical properties it is not used in deficient statistics.
3. If the average is in the degree, then compiling M.D. is difficult.
4. The main property is absent, it is not capable of further algebraic treatment.
5. It is not so easy to calculate for calculating X, M or Z and then for other measures.
6. If it is calculated from Z, it is not more reliable because the mode (Z) is not a true representative of the series.
7. As the signals are ignored, it is not mathematically possible. Algebraically we have to move forward for standard deviation; Or another measure of dispersion.
8. For the mean, open and series can not be taken for the right result.
9. If the limit increases in the case of sample increase, then the mean deviation also increases but not in the same proportion.

Conclusion  – Quartile deviation is related to median in its properties. This outer quartet takes into account the number of digits lying above or below the point, but not for their magnitude. It is useful with open-end distribution. In the middle deviation distribution, the precise position of each digit is kept in mind. The device gives a more accurate measurement of the spread of the deviation score but is mathematically insufficient. Mean deviation is affected by the fluctuation of the sample.

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