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Question
The mean of six numbers: x − 5, x − 1, x, x + 2, x + 4 and x + 12 is 15. Find the mean of first four numbers.
Solution
The mean of six numbers are x – 5, x – 1, x, x + 2, x + 4 and x + 12 is 15
∴ Mean =`(("x"-5)+("x"-1)+("x")+("x"+2)+("x"+4)+("x"+12))/6`
= `("x"-5+"x"-1+"x"+"x"+2+"x"+4+"x"+12)/6`
= `(12+6"x")/6=15`
⇒ 12 + 6x = 90
⇒ 6x = 90 − 12
⇒ 6x = 78
⇒ x = `78/6=13`
x = 13
∴ The six numbers are (13 − 5), (13 − 1), 13, (13 + 2), (13 + 4), (13 + 12) i.e. 8, 12, 13, 15, 17, 25
Now, mean of first four numbers =`(8+12+13+15)/4=48/4=12`
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