Question

the mean of 8 no. is 35.if a no. is excluded then the mean is reduced by 3.find the excluded number

Answer 1

Solution :-

The mean of 8 number is 35.

Sum of observations = 35 × 8 = 280

Given : A number is excluded then the mean is reduced by 3. Then the mean of 7 number becomes 35 - 3 = 32.

Sum of observations = 32 × 7 = 224

Number excluded = 280 - 224

= 56

Hence,

The excluded number = 56

Answer 2

Mean of 8 no.=35

$\tt{mean = \frac{sum \: of \: total \: terms}{total \: Numbers} } \\ \\ \tt{ \frac{sum \: of \: 8 \: terms}{8} = 35} \\ \\ \tt{sum \: of \: 8 \: terms = 35 \times 8} \\ \\ \mathtt{sum \: of \: 8 \: terms = 280}$

Now a Number Is Excluded (remove)

Mean Decrease by 3

Now Total Terms=7

Mean=35-3=32

$\tt {\frac{sum \: of \: 7 \: terms}{7} = 32} \\ \\ \tt{sum \: of \: 7 \: terms = 32 \times 7} \\ \\ \tt{sum \: of \: 7 \: terms = 224}$

Number Excluded=Sum of 8 terms-Sum of 7 terms

=280-224

=56

$\boxed{ \tt{ \huge{excluded \: \: number = 56}}}$