Question

The weights (in kg.) of $15$ students of a class are$\text{:38,42,35,37,45,50,32,43,43,40,36,38,43,38,47}$

(i) Find the mode and median of this data. (ii) Is there more than one mode?

Answer 1

Step 1: Find the median of the given observation

To find the median first we arrange the given data in ascending order ,

$32,35,36,37,38,38,38,40,42,43,43,43,45,47,50$

Median: The value of the middle-most observation is called the median of the data.

Here $\text{n=15}$, which is odd.

Where $\text{n}$ is the number of students.

Calculation of median :

∴ median $\text{=value of}\frac{({\text{n+1)}}^{th}\text{observation}}{2}$$=\frac{1}{2}(15+1)=\frac{1}{2}\left(16\right)=8$

Then, the value of $8^{th}\text{term=40}$

Hence the median is $40$

Step 2: Find the mode of the given observation

Mode : Mode is the value of the variable which occurs most frequently.

Hence, $38$ and $43$ both occurs $3$ times.

Hence, the modes of the given weights $38$ is and $43$ .

(ii) Yes, there are $2$ modes for the given weights of the students.