Question

Calculate the mean and the (sample) standard deviation of the four numbers: 2, 3, 6, 9

1

(a) Two numbers, a and b, are to be added to this set of four numbers, such that the mean is increased by 1 and the (sample) standard deviation is increased by 2.5. Find the values of a and b.

I want to the values of a and b

Answer 1

for first 4 numbers:

S.No	X1		X12
1	2.00		4.00
2	3.00		9.00
3	6.00		36.00
4	9.00		81.00
ΣX	20.00	ΣX2	130.00
=Σx/n=	5.00	s12=(Σx2-(Σx)2/n)/(n-1)=	10.000
		s1=√s12                                =	3.162

mean of the sample =5

and standard deviation =3.162

a) with new numbers a and b: Σx =20+a+b=(5+1)*6

20+a+b =36

a+b =16 ...............(1)

also new variance s² =(Σx² -(Σx)²/n)/(n-1) =(3.162+2.5)²

((130+a²+b²)-(36)²/6)/(6-1) =32.06

130+a²+b² =376.3

130+a²+(16-a)²=376.3

2a²-32a+9.7 =0

a =(32 -/+ √(32²-4*2*9.7))/(2*2) = 0.31 and 15.69

therefore a =0.31

and b=15.69