Question

The final marks in Mathematics of $30$ students are as follows:

$53,61,48,60,78,68,55,100,67,90,75,88,77,37,84,58,60,48,62,5644,58,52,64,98,59,70,39,50,60.$

(i) Arrange these marks in the ascending order, $30-39$ one group, $40-49$ second group; etc.

Now answer the following:

(ii) What is the highest score?

(iii) What is the lowest score?

(iv) What is the range?

(v) If $40$ is the pass mark, how many have failed?

(vi) How many have scored $75$ or more?

(vii) Which observations between $50and60$ have not actually appeared?

(viii) How many have scored less than $50$?

Answer 1

(i) Arrange the marks in groups of mentioned range:

There are eight groups namely $1to8$ is, $30-39,40-49,50-59,60-69,70-79,80-89,90-99,100-109$ respectively. The arranged numbers are as follows:

Group $1\left(30-39\right)-37,39$

Group $2(40-49)-44,48,48$

Group $3(50-59)-50,52,53,55,56,58,58,59$

Group $4(60-69)-60,60,60,61,62,64,67,68$

Group $5(70-79)-70,75,77,78$

Group $6(80-89)-84,88$

Group $7(90-99)-90,98$

Group $8(100-109)-100$

(ii) Find the highest score obtained:

The highest score obtained by any student is $100$

(iii) Find the lowest score obtained:

The lowest score obtained in exams is $37$

(iv) Find the range:

Range is the difference between the maximum and minimum marks obtained in the observation.

Range = $100-37=63$

So, range is $63$.

(v) Find the number of students failed:

As, there are only two students securing less than forty marks,

So the total number of students who failed is $2.$

(vi) Find the number of students securing 75 or more:

There are only $8$ students who secured more than or equal to $75$.

(vii) Find the number of students whose observation didn't occur:

The observations that really didn't appear are $51,54and57.$

(viii) Find the number of students who scored less than $50$ marks:

There are only $5$ students scored less than fifty marks in the exam.