[3 marks sum]

Question 13 Marks

The heights of $9$ persons are $142 cm, 158 cm, 152 cm, 143 cm, 139 cm, 144 cm, 146 cm, 148 cm$ and $151 cm.$ Find the mean height.

Answer

The heights are:
$142 cm , 158 cm , 152 cm , 143 cm , 139 cm , 144 cm , 146 cm , 148 cm , 151 cm $
$n =9 \\ \bar{x}=\frac{x_1+x_2+x_3+\ldots .+x_n}{n} $
$ \bar{x}=\frac{142+158+152+143+139+144+146+148+151}{9}$
$\bar{x}=\frac{1323}{9} $
$\bar{x}=147 cm$
The mean height $=147 cm$

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Question 23 Marks

If the mean of $8 , 14 , 20 , x$ and $12$ is $13,$ find $x.$

Answer

$\text { Numbers are }=8,14,20, x , 12$
$ \text { Mean }=13$
$n =5 $
$\bar{x}=\frac{x_1+x_2+x_3+\ldots .+x_n}{n} $
$ \Rightarrow 13=\frac{8+14+20+x+12}{5} $
$ \Rightarrow 13=\frac{54+x}{5} $
$ \Rightarrow 54+ X =65$
$ \Rightarrow x =11$
The value of $x=11$

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Question 33 Marks

Find the median of the following:
3x, x+5, x+7, x+9, x+11, x+13

Answer

$ 3 x, x+5, x+7, x+9, x+11, x+13 $
Arranging the given data in descending order:
$ x+13, x+11, x+9, x+7, x+5,3 x $
The middle terms are $x+9$ and $x+7$ which are 3rd and $4^{\text {th }}$ terms
$ \text { median }=\frac{x+9+x+7}{2}=\frac{2 x+16}{2}=x+8 $
Therefore, Median $=x+8$.

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Question 43 Marks

Find the median of the following:
25, 34, 31, 23, 22, 26, 35, 29, 20, 32

Answer

$ 25,34,31,23,22,26,35,29,20,32 $
Arranging the given data in descending order:
$ 35,34,32,31,29,26,25,23,22,20 $
The middle terms are 29 and 26 which are $5^{\text {th }}$ and $6^{\text {th }}$ terms
$ \text { median }=\frac{29+26}{2}=\frac{55}{2}=27.5 $
Therefore, Median of numbers $=27.5$

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Question 53 Marks

Find the rnedian of the first $15$ whole numbers .

Answer

The numbers are:
$7,8,9,10,11,12,13,14,15,16,17 $
$ \bar{x}=\frac{x_1+x_2+x_3+\ldots .+x_n}{n}$
$ n =11 $
$ \Rightarrow \bar{x}=\frac{7+8+9+10+11+12+13+14+15+16+17}{11}$
$\Rightarrow \bar{x}=\frac{132}{11}$
$\Rightarrow \bar{x}=12 $
Therefore, Mean of numbers from $7$ to $17=12$

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Question 63 Marks

Find the mean of all numbers from $7$ to $17.$

Answer

The numbers are:
$7,8,9,10,11,12,13,14,15,16,17$
$ \bar{x}=\frac{x_1+x_2+x_3+\ldots .+x_n}{n} $
$ n =11 $
$\Rightarrow \bar{x}=\frac{7+8+9+10+11+12+13+14+15+16}{11}+17 $
$ \Rightarrow \bar{x}=\frac{132}{11}$
$ \Rightarrow \bar{x}=12$
Therefore, Mean of numbers from $7$ to $17=12$

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Question 73 Marks

Find the mean of first $10$ prime numbers.

Answer

The first $10$ prime numbers are:
$ 2,3,5,7,11,13,17,19,23,29$
$ \bar{x}=\frac{x_1+x_2+x_3+\ldots+x_n}{n} $
$ n =10$
$ \Rightarrow \bar{x}=\frac{2+3+5+7+11+13+17+19+23+29}{10}$
$\Rightarrow \bar{x}=\frac{129}{10}$
$ \Rightarrow \bar{x}=12.9 $
Therefore, Mean of first $10$ prime numbers $=12.9$

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Mathematics [3 marks sum]

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