Question

The scores in Mathematics test (out of 25) of 15 Students are as follow 19,25,23,20,9,20,15,10,5,16,25,20,24,12,20 Find the made and median of this data?​

Answer 1

Answer :-

• The mode of the given data = 20.
• The median of the given data = 20.

Given :-

• The scores in Mathematics test (out of 25) of 15 students.

To find :-

• The mode and median of the given data.

Step-by-step explanation :-

• First let's find the mode of the given data!

We know that :-

• The observation which occurs more times than any other observation in a data is it's mode.

Here,

• 20 occurs more times than any other observation.

Hence,

• 20 is the mode of the given data.

________________________________

• Now let's find the median of the given data. Here, the number of observations is 15, which is odd.

We know that :-

$\underline{\boxed{\sf Median = \dfrac{n + 1}{2} \: th \: observation, when \: n\: is\: odd}}$

Where,

• n is the number of observations.

Here,

• Number of observations = 15.

Therefore,

$\rm Median = \dfrac{15 + 1}{2} \: th \: observation$

$\rm Median = \dfrac{16}{2} \: th \: observation$

$\rm Median = 8th \: observation$

Arranging the data in ascending order,

• 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25.

Here,

• The 8th observation is 20.

Therefore,

• 20 is the median of the given data.