Question

If sample mean of 10,14,x,y equals 10

And the sample mean for 15,23,-3, 2xy equals 12 find mean for 5,6,4,x

with explaination please. why and how?

my prof doesnt really explain well.

Thanks

Answer 1

Sample mean :-

(Sum of the all samples) / total no. of samples

Given:-

1) The sample mean of 10,14,x,y equals 10

which means: (10+14+x+y)/4 = 10

Do cross muliplication to the above equation and solve.

=> 24+x+y=40

=> x+y = 40-24

=> x+y = 16 -------------------------- (eq 1)

Here our first aim to get the values of x and y.

2) The sample mean for 15,23,-3, 2xy equals 12

By summing all the samples and dividing by total no samples.

=> (15 +23 - 3+2xy )/4 = 12

=> Solve by cross multiplication of 4 with 12

=> 35+2xy=12*4 = 48

=> 2xy = 48-35

=>2xy = 13 -----------------------> (eq 2)

=> By re arranging the terms xy =13/2

=> And Here we get y=13/2x

=>substitute y value in equation1 x+y = 16

=> x+13/2x =16

=> 2x² +13=16*2x

=> 2x² +13=32x

=> 2x^{2 -} 32x+13=0

Find roots:-

(-b + sqrt( b²-4ac) )/2a ,(-b - sqrt( b²-4ac) )/2a

a = 2, b = -32, and c = 13

=> (32 + sqrt((-32)² -4 * 2*13))/2 * 2, (32 - sqrt((-32)² -4 * 2*13))/2 * 2

=> (32 + sqrt(1024-104))/4, (32 - sqrt(1024-104))/4

=> x = 15.5829,0.417125

3) Finally finding mean for 5,6,4,x.

mean = (5+6+4+x)/4

=(15+x)/4 --------------------------> (eq 3)

substitute those values of x in eq 3

= (15+0.417125)/4 =3.85428125

(15+15.5829)/4 = 7.645725

mean =  7.645725 , 3.85428125

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The is the correct procedure of solving this problem.

If my answer is not correct please let me know in comment session. and kindly check the values in the question clearly.