Question 12 Marks
The mean of $18, 24, 15, 2x + 1$ and $12$ is $21.$ Find the value of $x.$
AnswerMean of given data $= \frac{18+24+15+2 x+1+12}{5}$
$\Rightarrow 21=\frac{70+2 x}{5}$
$ \Rightarrow 5 \times 21=70+2 x $
$ \Rightarrow 105=70+2 x $
$ \Rightarrow 2 x=105-70 $
$ \Rightarrow 2 x=35$
$\Rightarrow x=\frac{35}{2}$
$\Rightarrow x=17.5$
View full question & answer→Question 22 Marks
Find the mean of $8, 12, 16, 22, 10$ and $4.$ Find the resulting mean$,$ if each of the observations$,$ given above$, b:$ eincreased by $25\%$
AnswerNew Mean $=$ Original mean $+ 25\%$ of original mean
$\Rightarrow$ New mean $= 12 + 25\%$ of $12$
$\Rightarrow$ New mean $=12+\frac{25}{100} \times 12$
$\Rightarrow$ New mean $=12+\frac{1}{4} \times 12$
$ \Rightarrow$ New mean $=12+3 $
$ \Rightarrow$ New mean $=15$
View full question & answer→Question 32 Marks
The median of observations $10, 11, 13, 17, x + 5, 20, 22, 24$ and $53 ($arranged in ascending order$)$ is $18;$ find the value of $x.$
AnswerTotal number of observations $= 9 ($odd$)$
Now, if $n =$ odd
$\text { Median }=\left(\frac{n+1}{2}\right)^{\text {th }} \text { term }$
$\Rightarrow \text { Median }=\left(\frac{9+1}{2}\right)^{\text {th }} \text { term }=5^{\text {th }} \text { term }=x+5$
Now, Median $= 18 ... ($given$)$
$\therefore x + 5 = 18$
$\Rightarrow x = 13.$
View full question & answer→Question 42 Marks
Find the median of:
$241, 243, 347, 350, 327, 299, 261, 292, 271, 258$ and $257$
AnswerFirstly arrange the numbers in ascending order
$241, 243, 257, 258, 261, 271, 292, 299, 327, 347, 350$
Now since $n = 11 ($ Odd $)$
Median $=$ Value of $\left(\frac{n+1}{2}\right)^{\text {th }}$ term
$= 6^{th}$ term
$= 271$
Thus the median is $271.$
View full question & answer→Question 52 Marks
Find the median of: $25, 16, 26, 16, 32, 31, 19, 28$ and $35$
AnswerFirstly arrange the numbers in ascending order
$16, 16, 19, 25, 26, 28, 31, 32, 35$
Now since
$n = 9 ($odd$)$ Therefore the Median
$=\left(\frac{n+1}{2}\right)^{\text {th }} $
$=\left(\frac{9+1}{2}\right)^{\text {th }}$
$= 5^{th}$
Thus the median is $26.$
View full question & answer→Question 62 Marks
The mean of $15$ observations is $32$. Find the resulting mean$,$ if the observation is$:$ Decreased by $20\%$
AnswerGiven that the mean of $15$ observations is $32$
resulting mean decreased by $20\%$
$= 32 - \frac{20}{100} \times 32$
$= 32 - 6.4$
$= 25.6$
View full question & answer→Question 72 Marks
The mean of $15$ observations is $32$. Find the resulting mean $,$ if the observation is $:$ Increased by $60\%$
AnswerGiven that the mean of $15$ observations is $32$
resulting mean increased by $60\%$
$= 32 +\frac{60}{100} \times 32$
$= 32 + 19.2$
$= 51.2$
View full question & answer→Question 82 Marks
The mean of $15$ observations is $32.$ Find the resulting mean $,$ if the observation is $: $ Divided by $0.5$
AnswerGiven that the mean of $15$ observations is $32$
resulting mean divide by $0.5$
$=\frac{32}{5}$
$= 64$
View full question & answer→Question 92 Marks
The mean of $15$ observations is $32.$ Find the resulting mean$,$ if each observation is $:$ Multiplied by $2$
AnswerGiven that the mean of $15$ observations is $32$
resulting mean multiplied by $2$
$= 32 \times 2$
$= 64$
View full question & answer→Question 102 Marks
The mean of $15$ observations is $32.$ Find the resulting mean $,$ if the observation is $:$ Decreased by $7$
AnswerGiven that the mean of $15$ observations is $32$
resulting mean decreased by $ 7$
$= 32 - 7$
$= 25$
View full question & answer→Question 112 Marks
The mean of $15$ observations is $32$. Find the resulting mean $,$ if the observation is$:$ Increased by $3$
AnswerGiven that the mean of $15$ observations is $32$
resulting mean increased by $3$
$= 32 + 3$
$= 35$
View full question & answer→Question 122 Marks
Find the mean of $x + 3, x + 5, x + 7, x + 9$ and $x + 11.$
AnswerThe given values are $x + 3, x + 5, x + 7, x + 9, x + 11$
We know, Mean is given by,
Mean $=\frac{\text { Sum of the elements }}{\text { Total number of elements }}$
Here, number of observations $= 5.$
Mean $=\frac{x+3+x+5+x+7+x+9+x+11}{5} $
$ =\frac{5 x+35}{5}$
$= x + 7.$
View full question & answer→Question 132 Marks
Find the mean of all factors of $10.$
AnswerAll factors of $10$ are $1, 2, 5, 10$
The mean of all factors of $10$ are
$=\frac{1+2+5+10}{4} $
$ =\frac{18}{4} $
$ =4.5$
View full question & answer→Question 142 Marks
Find the mean of the first ten odd natural numbers.
AnswerThe first ten odd natural numbers are $1, 3, 5, 7, 9, 11, 13, 15, 17, 19$
The mean of the first ten odd numbers
$=\frac{\text { Sum }}{\text { Number of observations }} $
$ =\frac{1+3+5+7+9+11+13+15+17+19}{10} $
$ =\frac{100}{10}$
$= 10$
View full question & answer→Question 152 Marks
Find the mean of the first six natural numbers.
AnswerThe first six natural numbers are $1, 2, 3, 4, 5, 6.$
The mean of the first six natural numbers
$=\frac{1+2+3+4+5+6}{6}$
$=\frac{21}{6}$
$=3.5$
View full question & answer→Question 162 Marks
Find the mean of $43, 51, 50, 57$ and $54.$
AnswerThe numbers given are $43, 51, 50, 57, 54$
The mean of the given numbers will be
$=\frac{43+51+50+57+54}{5} $
$=\frac{255}{5}$
$=51$
View full question & answer→Question 172 Marks
Find x if $9, x, 14, 18 x, x, 8, 10$ and $4$ have a mean of $11.$
Answer$\text { Mean }=\frac{\text { Sum of observations }}{\text { Total number of observations }}$
$ \Rightarrow 11=\frac{9+x+14+18+x+x+8+10+4}{9}$
$\Rightarrow 11 \times 9 = 63 + 3x$
$\Rightarrow 3x + 63 = 99$
$\Rightarrow 3x = 99 - 63$
$\Rightarrow 3x = 36$
$\Rightarrow x = 12$
View full question & answer→Question 182 Marks
Find the mean of $75$ numbers, if the mean of $45$ of them is $18$ and the mean of the remaining ones is $13.$
AnswerMean of $45$ numbers $= 18$
$\Rightarrow $ Sum of $45$ numbers $= 18 \times 45 = 810$
Mean of remaining $( 75 - 45 ) 30 $ numbers $= 13$
$\Rightarrow $ Sum of remaining $ 30 $ numbers $= 13\times 30 = 390$
$\Rightarrow $ Sum of all the $75 $numbers $= 810 + 390 = 1200$
$\Rightarrow $ Mean of all the $75$ numbers $=\frac{1200}{75}=16$
View full question & answer→