Missing frequency 1

Missing frequency 1

1. PROGRAMME B.COM SUBJECT QUANTITATIVE TECHNIQUE – I SEMESTER III UNIVERSITY VIJAYANAGAR SRI KRISHNADEVARAYA UNIVERSITY, BALLARI SESSION 38

2. RECAP Mean, Median & Mode Under Continuous 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 - 38 Missing Frequencies & Variables in Mean Under Discrete Series Problems------ 01

6. Missing frequencies under discrete series Ex ; 1. Find missing frequency when Mean = 18 X: 5, 10, 15, 25, 30 F: 2, 6, f , 5, 4 Solution: X F fx 5 2 10 10 6 60 15 f 15f 25 5 125 30 4 120 N = 17 + f ∑ fx = 315 + 15f

7. CONTD = ∑ fx/n, ∑ fx = 315 + 15f, n = 17+f, = 18 18 = 315 + 15f / 17+f 18 (17 + f) = 315 + 15f 306 + 18f = 315 + 15f 18f – 15f = 315 – 306 3f = 9, f =9/3, f = 3 Ex; 2. Find Missing value when mean wage 111.85 Wage: 100, 110, X, 125, 130 workers 15, 12, 18, 12, 08 Solution; see next page  

8. CONTD Ascertaining of missing wages WAGES (X) WORKERS(F) FX 100 15 1500 110 12 1320 X 18 18X 125 12 1500 130 08 1040 N = 65 ∑ FX = 5360 + 18X

9. CONTD ∑ FX = 5360 + 18X, N= 65, = ∑ FX/N 111.85 = 5360 + 18X/ 65 111.85 X 65 = 5360 + 18X 7270.25 = 5360 + 18X 7270.25 – 5360 = 18X 1910.25 = 18X X = 1910.25/18 X =106.13 OR 106  

10. SUMMARY As we already discussed and learnt today on Measures of Central Tendency ( Averages) Missing Frequencies & Variables in Mean Under Discrete Series Problems ------ 01

11. MCQs 1 . The distribution in which mean = 50 and median =48 mode will be ____________ 44 24 34 None of these 2.  R elationship of empirical SK=mean – mode/ S .D Z = 3Me - 2 Mode = 3median – 2mean Both b and c  

12. MCQs 3 . If mean = 35 and Mode = 32 and Median = ? 34 32 Zero None of these 4. If median = 21.5 , Mode = 22 and Mean = ? 20 19 21.25 None of these

13. MCQs 5 . The relationship of empirical between averages Some time equal Never equal Always equal None of these

14. CONTD ANSWERS 1. A 2. D 3 . A 4. C 5. A

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