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

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