1. 1 “While an individual is an insolvable puzzle, in an aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man do, but you can say with precision what an average number will be upto”. -Arthur Conan Descriptive Measures

2. 2 Measures of Central Tendency Mean Median Mode

3. 3 Requisites of a good measure of central tendency 1. It should be easy to calculate and understand. 2. It should be rigidly defined. 3. It should be representative of the data. 4. It should have sampling stability. 5. It should not be affected by extreme values.

4. 4 Which measure is appropriate? A person who does not know how to swim has to cross a river from one bank to another by walking into the water with a stick. He tries to determine the length of stick on the basis of average length of river. Which measure of central location w.r.t the depth of the river will save him from getting drowned?

5. 5 Mean

6. 6 The FD below represents time in seconds needed to serve a sample of customers by a cashier at a discount store. Find the Mean.

7. 7 TimeFreqTimeFreq 20-30680-9011 30-401690-1007 40-5021100-1104 50-6029110-1200 60-7025120-1302 70-8022

8. 8 Properties of Mean 1. The sum of deviations of all individual observations from mean is always zero. 2. The sum of squares of deviations of observations about the mean is minimum. 3. Combine mean of set groups can be obtained.

9. 9 XX-MeanSqr (X-Mean)Sqr (X-10) 10-204000 20-10100 3000400 4010100900 50204001600 Mean=30Sum=0Sum=1000Sum=3000

10. 10 Limitations 1. Average may give a value that does not exist in data 2. Average may give absurd results 3. Does not give idea about difference in series 4. Affected by extreme values

11. 11 Weighted Arithmetic Mean

12. 12 Dave’s Giveaway Store advertises, “If our prices are not equal or lower than everyone else’s, you get it free.” One of Dave’s customers came into the store one day and threw on the counter bills of sale for six items she bought from a competitor for an average price less than Dave’s.

13. 13 The items cost : $1.29, $2.97, $3.49, $5.00, $7.50,$10.95. Dave’s prices for the same six items are $1.35, $2.89, $3.19, $4.98, $7.59, $11.50 Dave told, “My add refers to a weighted average price for the same items. Our average is low because our sales of these items have been: 7, 9, 12, 8, 6, 3.

14. 14 Is Dave getting himself into our out of trouble by talking about weighted average?

15. 15 Median

16. 16 Ungrouped distribution 251020303357

17. 17 31013173360

18. 18 Meridian Trucking company maintains records on all its rolling equipment. Here are weekly mileage records for its trucks. Calculate the median miles a truck travelled. 810450756789210657589488878689 1450560469890987559788943447775

19. 19 Median = 722.5 Miles

20. 20 Grouped distribution ClassFreqClassFreq 18-2212038-42184 22-2612542-46162 26-3028046-5086 30-3426050-5475 34-3815554-5853

21. 21 Median = 33.46

22. 22 Calculate median from the data pertaining to profits (in Cr.) of 125 companies: ProfitsNo. of comp ProfitsNo. of comp Less than 104Less than 5096 Less than 2016Less than 60112 Less than 3040Less than 70120 Less than 4076Less than 80125

23. 23 Median Profit = 36.25 Cr.

24. 24 Advantages Easy to calculate and understand Not effected by extreme observations Can be calculated for an open class Median can be found out for qualitative descriptions

25. 25 Disadvantages Does not depend on all observations Some accuracy is given up in choosing a single value to represent the distribution. Not capable of further algebraic treatment Not a good measure for estimation purpose since it is more affected by sampling fluctuations

26. 26 Properties Sum of absolute deviations from median is minimum X|X-med.||X-7| 443 621 801 1023 1245 Sum=12Sum=13

27. 27 Quartiles Deciles Percentiles

28. 28 Mode

29. 29 Calculate Mode ClassesFreq. Below 6012 60-6218 62-6425 64-6630 66-6810 68-703 70-723

30. 30 Measures of Variation Also called Dispersion. State the extent to which individual values differ from mean.

31. 31 Significance To determine reliability of an average To serve as a basis for the control of variability To compare two or more series with regard to there variability To facilitate the use of other statistical measures

32. 32 Absolute Variation Relative Variation

33. 33 Methods of studying Variation Range Inter-quartile Range or Quartile deviation Average deviation Standard deviation