A group of students was given a special test in Mathematics. The test was completed by the various students in the following time in (minutes) :

24, 30, 28, 17, 22, 36, 30, 19, 32, 18, 20, 24.

Find the mean time and median time taken by the students to complete the test.

By formula,

$\text{Mean} = \dfrac{\text{Total minutes}}{\text{No. of students}} \\[1em] = \dfrac{24 + 30 + 28 + 17 + 22 + 36 + 30 + 19 + 32 + 18 + 20 + 24}{12} \\[1em] = \dfrac{300}{12} \\[1em] = 25.$

Arranging the data in ascending order :

17, 18, 19, 20, 22, 24, 24, 28, 30, 30, 32, 36

Here, n = 12 which is even

By formula,

$\text{Median} = \dfrac{\dfrac{n}{2}\text{ th observation} + \Big(\dfrac{n}{2} + 1\Big) \text{ th observation}}{2} \\[1em] = \dfrac{\dfrac{12}{2}\text{ th observation} + \Big(\dfrac{12}{2} + 1\Big)\text{ th observation}}{2} \\[1em] = \dfrac{6 \text{ th observation} + 7\text{ th observation}}{2} \\[1em] = \dfrac{24 + 24}{2} \\[1em] = \dfrac{48}{2} \\[1em] = 24$

Hence, mean time = 25 minutes and median time = 24 minutes.