Question

The mean of 5 observations is 7.Later on it was found that two observations 4 and 8 were wrongly taken instead of 5 and 9.Find the correct mean
2

Answer 1

$\large{\underline{\rm{\purple{\bf{Given:-}}}}}$

Mean of 5 observations = 7

Incorrect observations were 4 and 8 and correct observations were 5 and 9

Sum of 5 observations = 35

$\large{\underline{\rm{\purple{\bf{To \: Find:-}}}}}$

The correct mean.

$\large{\underline{\rm{\purple{\bf{Analysis:-}}}}}$

$\sf Correct \ mean = \dfrac{Correct \ sum \ of \ 5 \ observations }{5}$

$\large{\underline{\rm{\purple{\bf{Solution:-}}}}}$

Given that,

Mean of 5 observations = 7

$\sf \dfrac{Sum \ of \ 5 \ observations }{5}=7$

Sum of 5 observations = 35

We know that, incorrect observations were 4 and 8 and correct observations were 5 and 9

Sum of incorrect observation = $\sf 4+8=12$

Sum of correct observations = $\sf 5+9=14$

Now, finding the correct sum of 5 observations

Correct sum of 5 observations = $\sf 3-12+14=37$

Hence, according to the analysis given

$\sf Correct \ mean=\dfrac{37}{5}= \underline{\underline{7.4}}$

Therefore, the correct mean is 7.4

$\large{\underline{\rm{\purple{\bf{To \: Note:-}}}}}$

The mean is the numerical average of the data set.

The mean is found by adding all the values in the set, then dividing the sum by the number of values.

Answer 2

Hope its helps you...!!