Question

Q.1 find the Median ,Mean and Mode of the following data 11,35,87,97,56,87,21,14,18,21,27,18,20,30

Answer 1

Answer:

mean $=38.714$

median $=24$

mode $=18,21,87$

Step-by-step explanation:

Mean is the total sum of the data divided by the number of the data.

That is mean $=$ total $/$ no. of terms

                      $=11+35+87+97+56+87+21+14+18+21+27+18+20+30 / 14\\\\=542/14\\\\=38.714$

Median is the middle most item. So first arrange the given data in ascending order

$11,14,18,18,20,21,21,27,30,35,56,87,87,97$

So the middle most item $=[\frac{n}{2} \ th\ observation+(\frac{n}{2} +1)\ th \ observation ]/2$

Here $n=14$ .

Therefore  median

                            $=[ \frac{14}{2} \ th\ observation + (\frac{14}{2} +1)\ th\ observation ]/2\\\\=[7th \ observation + 8th\ observation]/2\\\\= [21+27]/2\\\\=48/2=24$.

And mode is the most frequent item.

Here the numbers $18,21,87$ appeared $2$ times, therefore the data is multi-model.

Hence the answer.

thank you