1 / 31

GEOMETRIC MEAN

GEOMETRIC MEAN. Submitted to : Sir Umar. Work Distribution:. Ghayoor Abbas (Introduction) Awais Ghaffar ( Questionx..) Syed Saleh Haider (Geometric mean for ungroup data) Sohail Waqar ( Questionx of ungroup data) Sajawal Hussain (Geometric mean for group data)

elvis
Download Presentation

GEOMETRIC MEAN

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. GEOMETRIC MEAN Submitted to : Sir Umar

  2. Work Distribution: • Ghayoor Abbas (Introduction) • AwaisGhaffar(Questionx..) • Syed SalehHaider(Geometric mean for ungroup data) • SohailWaqar(Questionx of ungroupdata) • SajawalHussain(Geometric mean for group data) • M. Shoaib Malik (Questionxof group data)

  3. Definition :- The geometric mean ‘G’ of ‘n’ positive values is defined as the nth root of their product. Thus it is obtained by multiplying together all the ‘n’ values and then taking the nth root of the product. G =[ n: number of observations x: various values.

  4. The relation connecting arithmetic mean, geometric mean and harmonic mean Arithmetic Mean ≥ Geometric Mean ≥ Harmonic Mean

  5. Uses of Geometric Mean :- • Find the average percentage in sales, production etc. • Find the index numbers since it shows the relative change. • When large weights are given to small items and small weights are given to large items, the best measure of central tendency is Geometric Mean. That is, when there are extreme values, the best measure of central tendency to be used is Geometric Mean.

  6. Properties of geometric mean :- • The geometric mean is less than arithmetic mean, i.e. G.M<A.M. • The product of the items remains unchanged if each item is replaced by the geometric mean. • The geometric mean of the ratio of corresponding observations in two series is equal to the ratios of their geometric means. • The geometric mean of the products of corresponding items in two series is equal to the product of their geometric means.

  7. Merits And Demerits Of Geometric Mean :- Merits : • Geometric Mean is calculated based on all observations in the series. • Geometric Mean is clearly defined. • Geometric Mean is not affected by extreme values in the series. • Geometric Mean is amenable to further algebraic treatment. • Geometric Mean is useful in averaging ratios and percentages.

  8. Demerits : • Geometric Mean is difficult to understand. • We cannot compute geometric mean if there are both positive and negative values occur in the series. • We cannot compute geometric mean if one or more of the values in the series is zero.

  9. Question no 1:

  10. Question no 2 :

  11. Sequences :- • Arithmetic Sequence: Is a pattern of numbers where any term (number in the sequence) is determined by adding or subtracting the previous term by a constant called the common difference. Example: 2, 5, 8, 11, 14, 17 , 20 , 23 Common difference = 3 • Geometric Sequence: Is a pattern of numbers where any term (number in the sequence) is determined by multiplying the previous term by a common factor. Example: 2, 6, 18, 54, 162, 486 , 1458 , 4374 Common difference = 3

  12. Geometric Mean : Fact Consecutive terms of a geometric sequence are proportional. Example:Consider the geometric sequence with a common factor 10. 4 , 40 , 400 cross-products are equal (4)(400) = (40)(40) 1600 = 1600

  13. Therefore … To find the geometric mean between 7 and 28 ... label the missing term x 7 , ___ , 28 write a proportion cross multiply solve

  14. Geometric Mean (Ungroup-data) Formula : G = Antilog () where : Log x = log of x Σ logx = sum of (log x) values n = Total number of values

  15. Geometric Mean (Ungroup-data) Example : Find the geometric mean of the following values: 4, 6, 10, 15, 100. Step 1 : Find the log of the Given values

  16. Geometric Mean (Ungroup-data) Step 2 : Add the Values ∑logx = 0.6024 + 0.7781 + 1.0000 + 1.1760 + 2.0000 = 5.5505 Step 3 : Calculate the total numbers and there are 5 numbers, So n=5. Step 4 : Divide the values = ∑logx/n = 5.5505/5 = 1.1101 Step 5 : Taking Antilog = Antilog (1.1101) = 12.8854 Answer : Geometric Mean = 12.8854

  17. Question no 1

  18. Question no 2

  19. Geometric Mean (Group-data) Formula : G = Antilog ( ) where : Log x = log of given values (f.Logx) = Multiplying values of logx with f Σ (f.logx) = Sum of (f.logx) values Σf= sum of f (frequency)

  20. Geometric Mean (Group-data) Example : Find the geometric mean of the following data:Marks:  0-10, 10-20, 20-30, 30-40, 40-50No of Students (f) :  4, 8, 10, 6, 7 Step 1 : Find X through distribution of marks

  21. Geometric Mean (Group-data) Step 2 : Find the log of x

  22. Geometric Mean (Group-data) Step 3 : Multiply logx values with f Step 4 : Finding Σ (f.logx) by Adding the values of (f.logx) 2.7960+9.4088+13.9790+9.2646+11.5754= 47.0208

  23. Geometric Mean (Group-data) Step 5 : Find Σf By adding the values of f 4 + 8 +10 + 6 + 7 = 35 Step 6 : Find () 47.0208/35 = 1.3435 Step 7 : Taking Antilog () Antilog (1.3435) = 22.06 Answer : Geometric Mean = 22.06

  24. Geometric Mean (Discrete series) Formula : G = Antilog ( )

  25. Geometric Mean (Discrete series) Example 1: Calculate the geometric mean of the following data:X= 12 13 14 15 16 17.F= 5 4 4 3 2 1.

  26. Geometric Mean (Discrete series) f∑logx=21.6029 and N = 19 = Antilog of 21.6029/19 = Antilog of 1.1371 =13.71Answer: Geometric Mean = 13.71

  27. Question no 1 Find the geometric mean of the following data: Marks:  60-80, 80-100, 100-120, 120-140, 140-160, 160-180, 180-200.No of Students (f) :  5, 14, 17, 10, 1, 0

  28. Question no 2 Calculate the geometric mean of the following data:X= 1,2,3,4,5,6,7. F= 7,6,5,4,3,2,1.

  29. Any

More Related