Question

Following marks were obtained by $12$ students in a Mathematics test (out of $50$) :

$46,33,21,17,49,10,31,37,18,35,41,8$

What is the range of marks ?

Find the mean If the marks of the student who scored only $8$ marks are increased to $10$, find the new mean.

Answer 1

Step $1:$ Finding range

Given data, $46,33,21,17,49,10,31,37,18,35,41,8$

Now , $Range=Highestobservation-Lowestobservation$

So, Range, $49-8=41$

Step $2:$ Finding mean

Given data of $46,33,21,17,49,10,31,37,18,35,41,8$

Since, $Mean=\frac{Sumofallobservations}{TotalNumberofObservations}.....\left(i\right)$

Now, total number of observation $=12$ [ From the given data]

sum of all observation $=46+33+21+17+49+10+31+37+18+35+41+8=346$

So, Mean $=\frac{346}{12}=28.83$ [Using equation (i)]

Hence, mean of the boys is $28.83$

Step .$3:$ Finding mew mean when marks is increased from $8$ to $10$

If marks of a student is increased from $8$ to $10$ then sum of the observation will be increased by $2$

Hence, New sum of all observation $=46+33+21+17+49+10+31+37+18+35+41+10=348$

So, Mean $=\frac{348}{12}=29$

Hence, new mean will be $29$

Hence, Range is $41$, Mean is $28.83$ and new mean is $29$