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प्रश्न
The mean of 10 numbers is 24. If one number is included, the new mean is 25. Find the included number.
उत्तर
Let `barx` be the mean of n number of observation x1, x2, x3,..., xn
Mean of given data = `( x_1 + x_2 + x_3 + ... + x_n) / ( n )`
Given that mean of 10 numbers is 24.
That is,
`(x_1 + x_2 + x_3 +...+ x_10)/(10)`= 24
⇒ x1 + x2 + x3 + ... + x10 = 10 x 24
⇒ x1 + x2 + x3 + ... + x10 = 240
⇒ x1 + x2 + x3 + ... + x10 + x11 = 240 + x11 ....(1)
Also, given that mean of 11 number is 25.
That is,
`(x_1 + x_2 + x_3 +...+ x_10 + x_11)/(11) = 25`
⇒ x1 + x2 + x3 + ... + x10 + x11 = 11 x 25
⇒ x1 + x2 + x3 + ... + x10 + x11 = 275 ....( 2 )
From equations ( 1 ) and ( 2 ), we have :
x1 + x2 + x3 + ... + x10 + x11 = 240 + x11 = 275
240 + x11 = 275
⇒ x11 = 275 - 240 = 35
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