SChand CLASS 9 Chapter 15 Mean, Median and Frequency Polygon Exercise 15(B)

 Exercise 15 B 

Question 1

Ans : 2,3,5,7,9

Here h=5 which is odd 

If the median is the middle most term

So median = $\frac{n+1}{2}$ th term $=\frac{5+1}{2}$ th

$=3$ rd term which is 5

so median $=5$

Question 2

Sol: Here n=8 which is even 

If the median is the middle most term 

median = mean of $\frac{n}{2}$ th $\frac{n+1}{2}$ th 

$=\frac{1}{2}(4+h+5+h$ term $)$

$=\frac{1}{2}(16+20)=\frac{36}{2}=18$

Hence median $=18$

Question 3

Ans: Here number of terms n= 7 which is odd 

Arrange in Ascending  order,   

$33,44,148,51,60,61,63$

If median is the middle most term 

So median $=\frac{n+1}{2} \mathrm{th}$ term $=\frac{7+1}{2} \mathrm{th}$ term 

=4th term which is 51

Hence median =51

Question 4

Ans: Arranging is ascending order 

$8,10,11,13,116,17,19,22,25,31$

Here number of terms (n) = 10 which is even if the median is the middle most term 

So median $=\frac{1}{2}\left[\frac{n}{2}\right.$ th term $+\left(\frac{n}{2}+1\right)$ th term $]$

$=\frac{1}{2}\left[\frac{10}{2}\right.$ th term $+\left(\frac{10}{2}+1\right)$ th term $]$

$=\frac{1}{2}[5$ th term $+6$ th term $]$

$=\frac{1}{2}[16+17]=\frac{33}{2}=16.5$

So median $=16.5$

Question 5

Ans: First 10 prime number are  $2,3,5,7,11,13,17,19,23,29$

So Here n= 10 which is even 

So median = $=\frac{1}{2}\left[\frac{n}{2}\right.$ th term $+\left(\frac{n}{2}+1\right)$ th term $]$

$\begin{aligned}=& \frac{1}{2}\left[\frac{10}{2} \text { th term }+\left(\frac{10}{2}+1\right) \text { th term }\right] \\=& \frac{1}{2}[5 \text { th term }+6 \text { th term }] \\=& \frac{1}{2}[11+13]=\frac{24}{2}=12 \\ & \text { So median }=12 \end{aligned}$

Question 6

Ans: No of scores (n) = 13 which is odd 

35, 28 , 13 ,17 20 ,30,19,29,11,10,29,23 ,18,25,17

Arranging in ascending order 

$10,11,13,17,17,18,19,20,23,25,28,29,29,30,35$

$\begin{aligned} \text { median } &=\frac{n+1}{2} \text { th rerm }=\frac{15+1}{2} \text { th }=\frac{16}{2} \text { th } \\ &=8 \text { th term } \end{aligned}$

Which is 20 

So median =20 marks 

Question 7

Ans: Here $n=7$ which is odd

Arranging in descending order.

$5,15,25,35,45,55,60$

So median $=\frac{n+1}{2}$ th term $=\frac{7+1}{2}$ th term

$=4$ th term which is 35

So median marks $=35$

Question 8

Ans: No. of obervations $=16$ which is even

$\begin{aligned}&\text { So median }=\frac{1}{2}\left[\frac{n}{2} \text { th lerm }+\left(\frac{n}{2}+1\right) \text { thterm }\right] \\&\left.=\frac{1}{2}\left[\frac{16}{2} \text { th term }+\frac{16}{2}+1\right) \text { th term }\right] \\&=\frac{1}{2}[8 \text { th lerm }+9 \text { th term }] \\&=\frac{1}{2}(25+27)=\frac{52}{2}=26 \\&\text { So median }=26\end{aligned}$

Question 9

Ans: The observation are given in ascending order $8.9112,18(x+2),(x+1), 30,31,34.39$

Here $n=10$ which is even

$\text { So } \begin{aligned}\text { median } &=\frac{1}{2}\left[\frac{n}{2} \text { th term }+\left(\frac{n}{2}+1\right) \text { th term }\right] \\&\left.=\frac{1}{2}\left[\frac{10}{2} \text { th term }+\frac{10}{2}+1\right] \text { th term }\right] \\&=\frac{1}{2}[5 th \text { term }+6 \text { th term }] \\&=\frac{1}{2}[x+2+x+4] \\&=\frac{1}{2}[2 x+6]=x+3\end{aligned}$

But median is given $=24$

$\text { So } x+3=24 \Rightarrow x=24-3=21$

Question 10

Ans: (i) The data is given ascending order $18,20,25,126,30, x, 37,38,39,48$ Which are 10 an even number

$\begin{aligned}\text { So } \text { median } &=\frac{1}{2}\left[\frac{n}{2} \mathrm{th} \text { term }+\left(\frac{n{2}+1\right) \text { th term }\right] \\&=\frac{1}{2}\left[\frac{10}{2} \text { th term }+\left(\frac{10}{2}+1\right) \text { th term }\right] \\&=\frac{1}{2}[5 \text { th term }+6 \text { th term }] \\&=\frac{1}{2}[30+x]=\frac{30+x}{2}\end{aligned}$

But median is given $=35$

So $\begin{aligned} \frac{30+x}{2} &=35 \Rightarrow 30+x=70 \\ \Rightarrow x &=70-30=40 \end{aligned}$

(ii) By replacing 48 by 28 the terms will be 

$18,20,25,26,28,130,37,38,39,40$

New median $=\frac{1}{2}$ [5th term $+6$ th term $]$

$=\frac{1}{2}[28+30]$

$=\frac{58}{2}=29$

Hence new median $=29$