Question

the mean of 10 observations is 35 if one observation 32 was miss read as 23 find in you mean.​

Answer 1

$\dag\:\underline{\sf AnsWer :}$

• We have given a 10 observations whose mean is 35.
• One observation 32 was miss read as 23
• We need to find new mean.

$\qquad\bigstar\:\underline{\textbf{Sum of 10 observations}}$

$:\implies\sf Sum \: of \: 10 \: observation = 35 \times 10$

$:\implies \underline{ \boxed{\sf Sum \: of \: 10\: observation = 350}}$

As it is said in the question that , the one observation 32 was miss read as 23. Hence by removing that observation we get new total number of observation as 9.

$\qquad\bigstar\:\underline{\textbf{Sum of 9 observations}}$

$:\implies\sf Sum \: of \: 9 \: observation = 350 - 23$

$:\implies \underline{ \boxed{\sf Sum \: of \: 9 \: observation = 327}}$

$\qquad\bigstar\:\underline{\textbf{New mean :}}$

$\dashrightarrow\:\:\sf New \: mean = \dfrac{Sum \: of \: 9 \: observations + 32}{10}$

$\dashrightarrow\:\:\sf New \: mean = \dfrac{327 + 32}{10}$

$\dashrightarrow\:\:\sf New \: mean = \dfrac{359}{10}$

$\dashrightarrow\:\: \underline{ \boxed{\frak{New \: mean = 35.9}}}$

Answer 2

$\huge \tt \underline\purple{Correct \: Quéstion }$

• The mean of 10 observations is 35 if one observation 32 was miss read as 23 find new mean ?

$\huge \tt \underline\purple{Answer}$

$\sf Mean = \frac{ \: sum \: of \: the \: 10 \: observations \: }{10} \\\\\sf35 = \frac{\: sum \: of \: the \: 9 \: observations \: + \: 23 \: }{10} \\\\\sf sum \: of \: 9 \: observations = (35 \times 10) - 23 \\\sf = 327 \\\\\\\sf New \: mean = \frac{ \: sum \: of \: 9 \: observations \: + \: 32 \: }{10} \\\\ \sf = \frac{327 + 32}{10} \: = \frac{359}{10} \\\\\sf = \boxed{35.9} \\ \\ \\ \large\tt \underline\purple{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star\: Hence \: verified : ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$