Question

Mean of 5 observations is 6 and their standard deviation is 2. if the three observations are 5, 7 and 9 then find the other two observations.

Answer 1

Let the other two observations be x and y .

Therefore, the series is 1, 2, 6,x,y.

Now Mean x = 4.4 = (1+2+ 6 +x + y) /5

or 22 = 9 + x + y

Therefore

x + y = 13 ... (1)

Also

variance = 8.24 = (1/n) ∑ ( xi - x)2

⇒ 8.24 = (1/5)[ (3.4)2 + (2.4)2 + (1.6)2 + x2 +y2 – 2x(4.4)x (x + y) + 2x(4.4)2]

⇒ 41.20 = 11.56 + 5.76 + 2.56 + x2 + y2 – 8.8 x 13 + 38.72

Therefore x2 + y2 = 97 …....... (2)

But from (1), we have

x2 + y2 + 2xy = 169 …......... (3)

From (2) and (3), we have

2xy = 72 ... (4)

Subtracting (4) from (2), we get

x2 + y2 – 2 xy = 97 – 72

i.e. (x– y)2 = 25

or

x – y = ± 5 …..... (5)

So, from (1) and (5), we get

x = 9, y = 4 when

x – y = 5

or

x = 4, y = 9 when x – y = – 5

Thus, the remaining observations are 4 and 9.

Hope This Helps :)

Answer 2

Step-by-step explanation:

hope it will help you

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