Mean of 100 observations is 45. It was later found that two observations 19 and 31 were incorrectly recorded as 91 and 13. The correct mean is:

  • Option 1)

    44

  • Option 2)

    44.46

  • Option 3)

    45

  • Option 4)

    45.54

 

Answers (1)

As learnt in

ARITHMETIC Mean -

For the values x1, x2, ....xn of the variant x the arithmetic mean is given by 

\bar{x}= \frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}

in case of discrete data.

-

 

 Given that, 45 = \frac{x_{1}+ x_{2}+\cdot \cdot \cdot \ x_{100}}{100}

\therefore x_{1}+x_{2}+\cdot \cdot \ x_{100} = 4500

But two numbers (19+31 = 50) were incorrect

So, net sum = 4500 - 50 = 4450

Add correct numbers (91+13 = 104)

⇒ 4450 +104 = 4554

⇒ new mean = 4554/100 = 45.54


Option 1)

44

This option is incorrect

Option 2)

44.46

This option is incorrect

Option 3)

45

This option is incorrect

Option 4)

45.54

This option is correct

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