Question

arithmetic mean of 25 observationss is 10 if one of the observations is recorded as 60 instead of 50 find the correct mean

Answer 1

here is the answer of this ques

Answer 2

The correct mean is 9.6

Given,

Number of observations (N) = 25

Previous mean = 10

Incorrect data = 60

Correct data = 50

To Find,

The correct mean of 25 observations.

Solution,

Let the observations be x1, x2, ....., x25.

We know that, Mean = Sum of observations/Number of observations

⇒ Incorrect mean = 10 = (x1 + x2 +.....+ x25)/25

⇒ 10 = (x1 + x2 +.....+ x24 + 60)/25

⇒ 250 = x1 + x2 +.....+ x24 + 60

⇒ 250 - 60 = x1 + x2 +.....+ x24

⇒ x1 + x2 +......+ x24 = 190                                ---------------------------------------(1)

For the correct mean,

⇒ Mean = (x1 + x2 +.....+ x24 + 50)/25

putting sum of 24 terms from (1),

⇒ Mean = (190 + 50)/25

              = 240/25

              = 48/5

              = 9.6

Hence, the correct mean is 9.6

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