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Given, no of observations = n

And sum of deviation from 25 is 25 and sum of deviation from 35 is -25.

Let the actual mean be x,

We know that

Arithmetic mean,

Where, a is assumed mean.

In first case, where assumed mean, a = 25 and sum of deviation is 25, Putting values in formula

We have,

[1]

In first case, where assumed mean, a = 35 and sum of deviation is -25, Putting values in formula

We have,

[2]

Adding [1] and [2], we get

⇒ 2x = 60

⇒ x = 30

⇒ arithmetic mean of required data is 30.