Question

the mean of 40 numbers was found to be 38.later on it was detected that a number 56 was misread as 36. find the correct mean of the data

Answer 1

Answer:

$\green { Correct \: mean \: of \: data = 37.5}$

Step-by-step explanation:

$The \: mean \: of \: 40 \: numbers = 38$

$The \: sum \: of \: numbers = 40 \times 38\\=1520$

$If \: the \: number \: 56 \: is \: misread \:as\\36 \: then \: correct \: number = 56 - 36 \\= 20$

$Sum \: of \: correct \: numbers = 1520 + 20 \\= 1500$

$\green {Correct \: Mean = \frac{1500}{40}}\\= \green {37.5}$

Therefore.,

$\green { Correct \: mean \: of \: data} = \green {37.5}$

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Answer 2

Answer:

=> The correct mean is $38.5$

Step-by-step explanation:

Given that:-

The calculated mean of $40$ numbers = $38$

To find:- The correct mean,

Therefore,

By calculating the sum of these numbers

=> (38 × 40)

=> 1520  

So, the correct sum of these numbers:-

=> [1520 - (misread item) + (correct item)]

=> ( 1520 - 36 + 56 )

=> 1540.

Therefore, the correct mean

$=> \frac{1540}{40}$

=> 38.5

Hence, correct mean is 38.5