Quartile deviation

Quartile Deviation चतुर्थांश विचलन

1. By Dr. Abhishek Srivastava Quartile Deviation

2. Quartile: Meaning One of the three points that divide a data set into f o ur equ a l p a rt s . O r the v a l ues t h at di v ide dat a in t o g r o u p cont a ins equal n u mber of qu a rt e rs. Each observations or data. Median acts as base for calculation of quartile.

3. The quartile deviation is half of the difference between first quartile (Q1) and third quartile (Q3). This is also known as quartile coefficient of dispersion. QD = 𝑸𝟑−𝑸𝟏 𝟐 “A me asu r e of disp e r sion that i s def i ned as the va l ue half w ay bet w een the first and thi r d quartiles ( i . e., half t h e interquartile range). Also called semi-interquartile range” (APA). Garret (2014) defines, “the Quartile deviation or Q is half the scale distance between 75th and 25th percent is a frequency distribution”. According to Guilford (1963) the Semi inter Quartile range Q is the one half the range of the middle 50 percent of the cases. Quartile Deviation: Definition

4. So, this way we have three quartiles i.e. Q1, Q2 and Q3. Q1 – It is the midpoint of lowest 50% of data and also known as Lowest quartile or first quartile . Q2 – It is the median of the data or the middle point of a given data set and also known as second quartile . Q3 – It is the midpoint of highest 50% of data and also known as highest quartile or third quartile. Thus the quartile m easures the dispersion of score above and below the median by dividing the entire data set into four equal groups. Explanation

5. For Ungrouped Data(Hypothetical data) ( i ) If data is in odd number Ex – 12, 54, 32, 51, 24, 60, 21, 44, 31, 48, 50 Step I – Arrange the raw data in ascending order. Therefore, 12, 21, 24, 31, 32, 44, 48, 50, 51, 54, 60 Step II – Find out Q1 in the ordered distribution. therefore, Q1=11+1/4 = 3 rd position i.e. 24 Computation of QD

6. Step III – Find out Q3 Q3 = 𝑵+𝟏 𝟑 th position in the ordered distribution. 𝟒 therefore, Q3 = (11+1)3/4 = 9 th position i.e. 51 Step IV – Find out Semi-quartile range or QD Q = 𝑸𝟑−𝑸𝟏 𝟐 therefore, = 𝟓𝟏−𝟐𝟒 𝟐 = 27/2= 13.5

7. Computation of QD For Ungrouped Data(Hypothetical data) (i) If data is in even number Ex – 12, 54, 32, 51, 24, 60, 21, 44, 31, 48 Step I – Arrange the raw data in ascending order. Therefore, 12, 21, 24, 31, 32, 44, 48, 51, 54, 60 Step II – Find out Q1 Q1 = 𝑵 + 𝟏 𝟒 th position in the ordered distribution. therefore, Q1=11/4 = 2.75 th position i.e. 2 nd obs + .75 (3 rd obs -2 nd obs), 21+.75(24-21) = 21+ 1.5 = 22.5

8. Step III – Find out Q3 Q3 = 𝑵+𝟏 𝟑 th position in the ordered distribution. 𝟒 therefore, Q3 = (10+1)3/4 = 8.25 th position i.e. 8 th obs + .25(9 th obs – 8 th obs) = 51+.25(54-51) = 51+.25(3) => 51+.75 = 51.75 Step IV – Find out Semi-quartile range or QD 𝟐 Q = 𝑸𝟑−𝑸𝟏 therefore, 𝟓𝟏.𝟕𝟓−𝟐𝟐.𝟓 = 29.25/2 𝟐 = 14.625

9. Thanks