Question

The mean of 10 observation was found to be 30. However, later it was found that an observation 23 was misread as 32. Find the actual mean. ​

Answer 1

Answer : 29.1

Step by step explanation :

Mean of 10 observations = 30

Sum of 10 observations = 30 × 10 = 300

Sum of 10 observations = 300

Since, 23 was misread as 32,

Sum of new observations = [ 300 - (wrong observation + correct observation)

= ( 300 - 32 + 23 )

= 300 - 9

= 291

Correct mean = Sum of new observations / Total observations

= 291/10

= 29.1

Thus, the actual mean is 29.1

Answer 2

Answer:-

$\mathsf{Given, }$

$\mathsf{No \: of \: observations = 10}$

$\mathsf{Mean \: of \: 10 \: observations = 30 }$

$\mathsf{Mean \: of \: the \: given \: data \: is = }$

$\mathfrak{mean = \frac{sum \: of \: observations}{no \: of \: observations} }$

$\mathsf{30 = \frac{sum \: of \: observations}{10} }$

$\mathsf{sum \: of \: observations = 10 \times 30}$

$\mathsf{sum \: of \: observations = 300}$

$\mathsf{Also \: given \: 23 \: was \: misread \: as \: 32}$

$\textsf{To find the actual mean =}$

[ subtract 32 from sum of observations (300) ]

$\mathsf{300 - 32 = 268}$

[ Add 23 to 268 ]

$\mathsf{268 + 23 = 291}$

$\textsf{New mean :-}$

$\mathsf{mean = \frac{291}{10} }$

$\textsf{mean = 29.1}$

Therefore mean of the given data is 29.1