The document provides examples and explanations of calculating basic statistics such as mean, median, and regression equations. It gives step-by-step workings for finding the geometric mean, harmonic mean, and regression lines from sets of data. It also explains concepts such as variance, covariance, quartiles, and determining if equations represent valid regression lines.

1. BASIC STATISTICS FOR NON COMMERCE STUDENTS by : DR. T.K. JAIN AFTERSCHO ☺ OL centre for social entrepreneurship sivakamu veterinary hospital road bikaner 334001 rajasthan, india [email_address] mobile : 91+9414430763

2. Find geometric mean of 3,6,12 In order to find geometric mean, first multiply them together : 3*6*12 = 216 now find factors of 216: 2*2*2*3*3*3 thus we have 2 and 3 coming three times. We have 3 numbers so we will take up that factor which comes three times or triple root of 216 = 2*3 = 6 answer.

3. Find harmonic mean of 4,6,10 In order to find harmonic mean, first use 1/4, 1/6 and 1/10, now add them : we get : (30+20+12)/120 = 62/120 now multiply it by 1/3 (as there are 3 numbers) : 62/360 now reverse it : 360/62 we get : 5.8 answer

4. Find 2 regression equations from following data?

5. STEPS IN REGRESSION Basic equation : Y = A + BX XY = AX+BX^2 in these equation, we have to find values of A and B. First of find out covariance and variance B = covariance / variance of x on the basis of B, find value of A.

6. Steps in regression 1. find DX and DY – DX is difference in each value of X with reference to the average value in X and DY is difference of each value in Y from the average of Y. 2. Find DX^2, DY^2, DXDY. 3. the average of DX^2 is variance of X and average of DY^2 is variance of Y. Average of DXDY is covariance of X and Y. 4 divide covariance by variance of X we get B.

7. solution.... Covariance in our example is : - .67 variance in our example : .67 thus B =-1 put the value of B in the first equation : Y = A + BX here Y (average of Y) = 3, and X = (average of X) = 3 thus : 3= A+(-1)*3, we get A = 6, thus our regression equation is ready.

8. Given the regression equations : 3X+Y=13 and 2X+5Y=20, which is the regression equation of Y on X? First equation : Y = 13- 3X 2 nd equation : Y = 4-2/5X square roots of products of B should be between -1 and 1. so try : (-3 * -2/5) = (-) 1.20, its square root is : 1.09, so this is not possible. However, only 2 nd equation can be taken up as its value is .4 which is between -1 and 1.

9. Given the following equation : 2x-3y = 10, 3x+4y=15, which is regression equation of X on Y? X = 5+3/2Y here B is 1.5 X = 5-4/3Y here B is -1.33 B should be between -1 and +1, so both the equations are not valid regression equations.

10. Y on X is : Y =-2X+3 and that of X on Y is 8X=-Y+3, what is coefficient of correlation? B in the first equation is : -2 and in second equation is -1/8, now multiply them, we get : 1/4, which gives us ½ or .5 as answer. As both the values are negative, the answer should be -.05

11. If AM and HM for 2 numbers are 5 and 3.2 respectively, then the GM will be ? Options: 4.1, 4.05, 4 Solution : GM = gm of AM and HM, thus : sqrt (5*3.2) = 4 the two numbers must be 2 and 8. answer

12. What is the value of first quartile for the observations 15,18,10, 20,23,28,12 and 16. options : 17,16,15.75,12 Put these in proper order : 10,12,15,16,18,20,23,28 as there are 8 numbers, so we will divide it by 4, we get (8+1)/4 = 2.25, thus answer is 12 + (.25* (15-12) ) = 12.75 answer

13. If there are 2 groups containing 30 and 20 observations and having 50 and 60 as AM then the combined AM ? Total : ((30*50) + (20*60)/(30+20) =2700/50 =54 answer

14. Average salary of a group of unskilled workers is 10000, that of a group of skilled workers is 15000, if the combined salary is Rs. 12000, what is the % of skilled workers? Options : 40,50,60 Let us try with 60 : 60% of 10000 = 6000 40% of 15000 = 6000 total =12000 answer

15. What is the HM of 1, 1/2, 1/3,...1/n? Options : n, 2n, 2/(n+1), n(n+1/2) Take any value of N and find the answer- HM, you find the same answer using the formula : 2/(n+1), so this is the answer

16. If there are 2 groups with 75 and 65 as HM and containing 15 and 13 observation the combined HM is given by ? Options : 65, 70.36, 70, 71 1970/28 = 70.36 answer

17. An aeroplane flies from A to B @500 km per hour and comes back from B to A @700 KM per hour, the average speed of the aeroplane is ? Find HM (harmonic mean of 700 and 500). 583.33 answer

18. If AM and GM for 10 observations are both 15, then the value of HM is ? Also 15. answer

19. If Rx and Ry denote ranges of X and Y respectively, where X and Y are related by 3x+2Y+10=0, what will be relation between X and Y? Options : Rx=Ry, 2Rx=3Ry, 3Rx=2Ry, Rx=2Ry 3Rx=2Ry answer

20. What is the coefficient of range for the following distribution:

21. solution... Fomula of range = (highest – least) / (highest + least) * 100 first convert the series to continuous series and then solve it. (59.5 – 9.5) / (59.5 + 9.5) * 100 = 72.46% answer

22. THANKS.... GIVE YOUR SUGGESTIONS AND JOIN AFTERSCHOOOL NETWORK / START AFTERSCHOOOL NETWORK IN YOUR CITY [email_address] PGPSE – WORLD'S MOST COMPREHENSIVE PROGRAMME IN SOCIAL ENTREPRENEURSHIP