The marks $(out\ of\ 100)$ obtained by a group of students in a science test are 85, 76, 90, 85, 39, 48, 56, 95, 81 and 75. Find the:
$(i)$. Highest and the lowest marks obtained by the students.
$(ii)$. Range of the marks obtained.
$(iii)$. Mean marks obtained by the group.

Given:

The marks (out of 100) obtained by a group of students in a science test are 85, 76, 90, 85, 39, 48, 56, 95, 81 and 75.

To do:

We have to find the:

(i) Highest and the lowest marks obtained by the students.

(ii) Range of the marks obtained.

(iii) Mean marks obtained by the group.

Solution:

Marks obtained by the group of students are $85, 76, 90, 85, 39, 48, 56, 95, 81, 75$

(i) Highest marks obtained by the student $=95$

Lowest marks obtained by the student $=39$

(ii) Range of the marks obtained $=$ Highest marks $-$ Lowest marks

$=95-39$

$=56$

(iii) Mean marks $=\frac{ \text { Sum of marks }}{ \text { Total number of students }}$

$=\frac{(85 + 76 + 90 + 85 + 39 + 48 + 56 + 95 + 81 + 75)}{10}$

$=\frac{730}{10}$

$=73$

Thus, the mean marks obtained by the group of the students is $73$.