# Quartile Deviation

Quartile deviation is the difference between the first and third quartiles. Quartile deviation is half the interquartile range. The interquartile range is the 75th percentile minus the 25th percentile. The 75th percentile is the number such that no more than 75% of the observations (or distribution mass) is less than it, and no more than 25% of the observations are greater than it (if a range of numbers satisfy this criterion, there are various conventions for picking a single number). The 25th percentile is defined in parallel fashion.

Quartiles are the values that divide a list of numbers into quarters.

• Put the list of numbers in order
• Then cut the list into four equal parts
• The Quartiles are at the cuts. Example: 5, 7, 4, 4, 6, 2, 8

Put them in order: 2, 4, 4, 5, 6, 7, 8

Cut the list into quarters

And the result is-

• Quartile 1 (Q1) = 4
• Quartile 2 (Q2), which is also the Median, = 5
• Quartile 3 (Q3) =
• Quartile deviation is based on the lower quartile Q1 and the upper quartile Q3. The difference Q3−Q1 is called the inter quartile range. The difference Q3−Q1 divided by 22 is called semi-inter-quartile range or the quartile deviation. Thus Q.D=Q3−Q12

### Merits of Quartile Deviation

(i) It can be easily calculated and simply understood.

(ii) It does not involve much mathematical difficulties.

(iii) As it takes middle 50% terms hence it is a measure better than Range and Percentile Range.

(iv) It is not affected by extreme terms as 25% of upper and 25% of lower terms are left out.

(v) Quartile Deviation also provides a short cut method to calculate Standard Deviation using the formula 6 Q.D. = 5 M.D. = 4 S.D.

(vi) In case we are to deal with the center half of a series this is the best measure to use.

### Demerits or Limitation Quartile Deviation

(i) As Q1 and Q3 are both positional measures hence are not capable of further algebraic treatment.

(ii) Calculation are much more, but the result obtained is not of much importance.

(iii) It is too much affected by fluctuations of samples.

(iv) 50% terms play no role; first and last 25% items ignored may not give reliable result.

(v) If the values are irregular, then result is affected badly.

(vi) We can’t call it a measure of dispersion as it does not show the scatterness around any average.

(vii) The value of Quartile may be same for two or more series or Q.D. is not affected by the distribution of terms between Q1 and Q3 or outside these positions.

So going through the merits and demerits, we conclude that Quartile Deviation cannot be relied on blindly. In the case of distributions with high degree of variation, quartile deviation has less reliability.

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