Question

the mean of 40 observations was 160. it was detected on rechecking that the value of 165 was wrongly copied as 125 for computation of mean .find the correct mean

Answer 1

Answer:

The correct mean of the required observations is 161.

Step-by-step explanation:

Mean = sum/no. *of observation

So,

= >  160 = sum of 40 observations/40

= >  40 x 160 = sum of 40 observations

= >  6400 = sum of 40 observations.

Later on, it was detected on rechecking that the value of 165 was wrongly copied as 125 for computation of mean.

So,

Correct sum of observations = 6400 - 125 + 165 = 6400 + 40 = 6440

Therefore,

Correct mean = correct sum of observations/40

Correct mean = 6440/40 = 161

Hence, the correct mean is 161.

Answer 2

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$\huge{\mathfrak{Here\:is\:ur\:answer}}$

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$\sf{\large{Let \:x \:be \:the \:incorrect\:mean }}$







As we know that,




♏$Incorrect\:Mean=Incorrect \:Sum\:of\:all\: observations/Total\: no \:of \:observations$




So,




•°•As incorrect mean is given we can find the incorrect sum






•°•$<b>Incorrect sum = incorrect Mean of 40 observations×40</b>$





•°•. Incorrect sum = 40×160=6400





•According to question it was the value of 165 is wrongly copied as 125, so




$<b>Correct sum= Incorrect sum of40 observations - Incorrect reading + correct reading</b>$




•°•$\sf{\bold{Then \:, Correct \:sum \:= 6400 - 125 + 165=6440}}$

$\sf{\boxed{correct\:mean=correct\: sum\:of \:40\:obse ration/40}}$





•°•So, the mean = Sum of correct observations/40
= 6440/40=161




$\bf{\boxed{So,\: the\: correct \: mean\: of\: 40 \:observations\: = 161}}$

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