Question

The mean weight of a group of 15 students is 62.5kg. If a new student is added and he weighs 75kg what is the new mean?

Answer 1

$\huge\boxed{\fcolorbox{purple}{ink}{Answer}}$

Original mean = 62.5 kg

Original number of students = 15 students

We know that,

${\sf{Mean\: =\: {\dfrac{Sum\: of\: weight\: of\: students}{Total\: no\: of\: students}}}}$

${\sf{\implies\: 62.5\: =\: {\dfrac{Sum\: of\: weight\: of\: students}{15}}}}$

${\sf{\implies\: Sum\: of\: weight\: of\: students\: =\: 62.5\: \times\: 15}}$

= 937.5 kg

New sum of weight = 937.5kg + 75kg = 1012.5 kg

New no. of students = 15 + 1 = 16

${\sf{New\:Mean\: =\: {\dfrac{New\:sum\: of\: weight}{New\:total\: no\: of\: students}}}}$

${\sf{\implies\: New\:Mean\: =\: {\dfrac{1012.5}{16}}}}$

= 63.28 kg

${\bold{\boxed{\blue{New\: Mean\: =\: 63.28 kg}}}}$