Question

The scores in Mathematics
test (out of 25) of 15
students is as follows: 19,
25,23,20,9,20,15,10,5,16,25,2
0,24,12,20 Find the mode
and median of this data? *​

Answer 1

Given :

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

To find :

• Mode &
• Median

According to the question,

Arranging the given data in ascending order :

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

So,the mode is 20 as it occurs most of the times.

Median :

For even : $\sf{ (\dfrac{n}{2} ) {}^{th} \: observation }$

For odd : $\sf{ (\dfrac{n}{2} + 1 ) {}^{th} \: observation }$

So,the number of observation is 15 [ which is odd ]

$\implies \sf{ (\dfrac{15}{2} + 1 ) {}^{th} \: observation }$

$\implies\sf{ \cancel\dfrac{16}{2} {}^{ \: \: 8} \: observation}$

$\implies\sf{8 {}^{th} \: observation}$

Now here we will find the number which is in 8th observation,

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

So,the median is 20 as it is in 8th observation.

Answer 2

$\huge {\underline{\pink{Given}}}$

The scores of mathematics test of students.

And the scores are:-

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

$\Large\bf\underline\red{Solution:-}$

To find the Mode and Median of the data we first have to arrange it in either Asending or Descending order.

$\bf\underline\blue{Arranging\:the\:data\:</p><p>in\: Asending\:order}$

$\longrightarrow$$5,9,10,12,15,16,19,20,20,20,20,23,24,25,25$

i)Now let us find the Mode of the data

first.

On arranging the data we get to know that $20$ occurs most of the time.

So,the$\boxed{\fcolorbox{black}{yellow}{Mode}}$of the data is $20$.

ii)Now we will find the Median of the data

Here on observing the data we get to know that it is Odd.

So,we will put the formula$\frac{n+1}{2}$

$\longrightarrow$$\frac{15+1}{2}$

$\longrightarrow$$\frac{16}{2}$

$\longrightarrow$${8}$

Therefore we will see the 8th observation of the data.

And the number is $20$

Hence,

The$\bf\underline\green{Mode}$is$20$

And the $\bf\underline\red{Median}$ is also $20$.

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