NCERT Class XI Mathematics - Statistics - Solutions
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Question : 28
Total: 34
The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.
Solution:
Let the remaining two observations be x and y. Then we are given that
⇒ 60 + x + y = 72 ⇒ x + y = 12 ... (i)
Also,
( 6 2 + 7 2 + 10 2 + 12 2 + 12 2 + 13 2 + x 2 + y 2 ) − ( 9 ) 2
⇒
( 36 + 49 + 100 + 144 + 144 + 169 + x 2 + y 2 ) − ( 81 )
⇒ 642 +x 2 + y 2
⇒x 2 + y 2
Now( x + y ) 2 + ( x – y ) 2 2 ( x 2 + y 2 )
⇒( 12 ) 2 + ( x – y ) 2
⇒( x – y ) 2 ( x – y ) 2
When x – y = 4 and x + y = 12, we get x = 8 and y = 4
When x – y = – 4 and x + y = 12, we get x = 4 and y = 8.
So, the remaining two observations are 4 and 8.
⇒ 60 + x + y = 72 ⇒ x + y = 12 ... (i)
Also,
⇒
⇒ 642 +
⇒
Now
⇒
⇒
When x – y = 4 and x + y = 12, we get x = 8 and y = 4
When x – y = – 4 and x + y = 12, we get x = 4 and y = 8.
So, the remaining two observations are 4 and 8.
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