Question

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:

1. Highest and lowest marks obtained by the students.
2. Range of the marks obtained.
3. Mean marks obtained by the group.

Answer 1

First arrange the marks of students in ascending order.
For part (1), the first marks in the ascending order will be the lowest marks, and the last marks in the order are the highest marks obtained by the students.
For part (2), use the formula of range, Range = Highest Marks – Lowest Marks. Substitute the marks and find the range.
For part (3), to find mean marks use the formula $Mean =$ $\dfrac{\text{Sum of Marks}}{\text{ Number of students}}$

Complete step-by-step answer:

1. The marks obtained by a group of students are 85, 76, 90, 85, 39, 48, 56, 95, 81, 75.
   Now, arrange the marks in ascending order.
   39, 48, 56, 75, 76, 81, 85, 85 , 90, 95
   Here, we can see the last marks in the ascending order is 95 and the first marks are 39.
   Hence, the highest marks are 95 and the lowest marks are 39.
2. The range is the difference between the highest and lowest marks.
   Range = Highest Marks – Lowest Marks
   Substitute the values,
   $\Rightarrow$Range $= 95 - 39$
   Subtract the values on the right side,
   $\therefore$Range $= 56$
   Hence, the range is 56.
3. We know that mean is given by
   $Mean =$ $\dfrac{\text{Sum of Marks}}{\text{ Number of students}}$………...….. (1)
   The sum of the marks is,
   $\Rightarrow 39 + 48 + 56 + 75 + 76 + 81 + 85 + 85 + 90 + 95 = 730$
   The number of students is 10.
   Substitute these values in equation (1),
   Mean $= \dfrac{{730}}{{10}}$
   Cancel out the common factors,
   $\therefore$Mean $= 73$
   Hence, the mean marks of the student are 73.

Note: The mean of the data calculates the central value of the data. It is also known as average. Students generally make mistakes in the calculation part of the mean, so it has to be done carefully. The range of the data gives the difference between the highest and the lowest value.