Range, Q.D and Co-efficient 2
- 1. PROGRAMME B.COM SUBJECT QUANTITATIVE TECHNIQUE – I SEMESTER III UNIVERSITY VIJAYANAGAR SRI KRISHNADEVARAYA UNIVERSITY, BALLARI SESSION 43
- 2. RECAP • Range, Quartile Deviation and Co efficient Under Individual and Discrete Series Problems------ 02
- 3. LEARNING OBJECTIVES • After reading this chapter, a student will be understand different measures of central tendency and Dispersion, i.e., Arithmetic Mean,Mean,Mode, Geometric and Harmonic mean & Range, Mean Deviation, Standard Deviation, Quartile Deviation, Co efficient of variation
- 4. LEARNING OUTCOMES • After the Chapter, The Students Shall be able to Differentiate, Determine, and Identify the relationships among Averages under Different Series of Data and too State the Merits and Demerits of Three Measures. The Students will apply Measures of Dispersion to Sample Population Data by Contrasting the Values of Standard Deviation & The Mean Deviation, Synthesizing the Mean,Standard,and Quartile Deviations into a Useful Description of a Set of Data
- 5. SESSION - 43 • Range, Quartile Deviation and Co efficient Under Continuous Series Problems - 02
- 6. Range and Quartile Deviation Example; 1 Calculate Range and Quartile deviation and coefficient of quartile deviation from the following distribution. Weekly Wages 5-7, 8-10, 11-13, 14-16, 17-19 No. of Workers 14, 24, 38, 20, 04 Solution; the above data convert into inclusive into exclusive method (i.e., 4.5 – 7.5, 7.5 – 10.5 so on)
- 7. CONTD Calculation of Range and Quartile deviation and coefficient of quartile deviation wages frequency C.F 4.5 -7.5 14 14 7.5 – 10.5 24 38 10.5 – 13.5 38 76 13.5 – 16.5 20 96 16.5 – 19.5 04 100 N = 100
- 8. Contd Q1 = L + N/4 – CF x C , Q3 = L + 3(N/4) – CF x C f f The item of N/4 = 100/4 =25th lies in Class interval 7.5 – 10.5, L= 7.5, C.F =14, F=24, C = 3 Q1 = 7.5 + 25 – 14 x 3 Q1 = 7.5+ 11/24 x 3 24 Q1 = 8.875 OR 9 The item of 3(N/4) = 3(100/4)= 300/4 =75th item lies in Class interval 10.5 – 13.5, L =10.5, CF =38, f =38, C =3 Q3 =10.5 + 75 – 38 x C, Q3 = 10.5 + 37/38 x 3 38 Q3 = 13.42
- 9. CONTD R = L – S R = 19.5 – 4.5 =15 Q3 – Q1 Co efficient of Q.D = Q3 + Q1 = 13.42 – 9/13.42 + 9 = 4.42/ 22.42 = 0.197 QUARTILE DEVIATION = Q3 – Q1/2 = 13.42 – 9/2 = 2.21 Co efficient of Range = L – S/L + S = 19.5 – 4.5/ 19.5 +4.5 = 0.625
- 10. CONTD Calculate quartile deviation from the following Solution: QUARTILE DEVIATION = Q3 – Q1/2 Q1 = L + N/4 – CF x C , Q3 = L + 3(N/4) – CF x C f f To compute quartiles, Qj or Q1 OR Q3 class = (Nth/4) item
- 11. CONTD
- 12. CONTD QUARTILE DEVIATION = Q3 – Q1/2 Quartile Deviation = 37.03 – 14.1/2 = 11.465 Q3 – Q1 Co efficient of Q.D = Q3 + Q1 = 37.03 – 14.1/ 37.03 + 14.1 = 0.22
- 13. MCQs I. If the maximum value in a series is 25 and its range is 15, the maximum value of the series is: (a) 10 (b) 15 (c) 25 (d) 35 II. Half of the difference between upper and lower quartiles is called: (a) Interquartile range (b) Quartile deviation (c) Mean deviation (d) Standard deviation III. If Q3=20 and Q1=10, the coefficient of quartile deviation is: (a) 3 (b) 1/3 (c) 2/3(d) 1
- 14. MCQs IV. If the observations of a variable X are, -4, -20, -30, -44 and -36, then the value of the range will be: (a) -48 (b) 40 (c) -40 (d) 48 V. Which measure of dispersion can be computed in case of open-end classes? (a) Standard deviation (b) Range (c) Quartile deviation (d) Coefficient of variation
- 15. REFERENCES • S.P. Gupta, Sultan Chand and Sons Publications, 2017 • S. C. Gupta, Himalaya Publishing House, Fundamentals of Statistics, 2018 • R.S.N Pillai and Bagavathi, S.Chand publications, 2010
- 16. THANK YOU