Question

The following 10 observations are arranged in the
ascending order as follows:
2 ,3, 5, 9, x + 1, x + 3, 14, 16, 19, 20.
If the median of the data is 11, find the value of x.​

Answer 1

Answer:

X=9

Step-by-step explanation:

since the observations are arranged in ascending order the median is equal to average of the two middle terms.

11=x+1+3+x÷2

22=2x+4

22-4=2x

18=2x

x=9

Answer 2

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\pink{\:\:\:\:\:\:\:Given:-\:\:\:\:\:\:\:}}$

$\sf:\bullet\:\: observation\: arranged\:in\: ascending\:order\\ \\ \sf:\implies 2,\:3,\:5,\:9,\:x+1,\:x+3,\:14\:,16,\:19,\:20\\ \\ \sf:\hookrightarrow median=11$

• We have to find the value of x

Now

$\star{\boxed{\sf{Median=\dfrac{\bigg(\dfrac{n}{2}\bigg) th\:term+\bigg(\dfrac{n}{2}+1\bigg)th\:term}{2}}}}$

Where n is the number of observation

n=10

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

$\sf:\implies 11=\dfrac{\bigg(\dfrac{n}{2}\bigg)th\:term+\bigg(\dfrac{n}{2}+1\bigg)th\:term}{2}\\ \\ \sf:\implies 11=\dfrac{\bigg(\dfrac{10}{2}\bigg)th\:term+\bigg(\dfrac{10}{2}+1\bigg)th\:term}{2}\\ \\ \sf:\implies 11=\dfrac{\bigg(\cancel{\dfrac{10}{2}}\bigg) term+\bigg(\cancel{\dfrac{12}{2}}\bigg)term}{2}\\ \\ \sf:\implies 11=\dfrac{5th\:term+6th\:term}{2}\\ \\ \sf:\implies 11\times 2=5th\:term+6th\:term\\ \\ \sf:\bullet 5th \:term= x+1\\ \sf:\bullet 6th\:term=x+3\\ \\ \sf:\implies 22=x+1+x+3\\ \\ \sf:\implies 22=2x+4\\ \\ \sf:\implies 22-4=2x\\ \\ \sf:\implies 18=2x\\ \\ \sf:\implies \cancel{\dfrac{18}{2}}=x\\ \\ \sf:\implies x=9$

$\huge{\boxed{\sf{x=9}}}$