Question 13 Marks
If the mean of $7, 16, 9, 15, 16, a, 12, 8, b, 11$ is $12,$ write a in terms of $b.$
AnswerMean$ =\frac{\sum x}{N} $
$=\frac{7+16+9+15+16+a+12+8+b+11}{10} $
$ \therefore 12=\frac{94+a+b}{10}$
$ \Rightarrow 120=94+a+b $
$\Rightarrow a=120-94-b=26-b $
$ \therefore a=26-b .$
View full question & answer→Question 23 Marks
The height of $8$ students $X$ in centimetres are given below:$148, 162, 160, 154, 170, 162, x, 152.$If the mean height is $158,$ find $x.$
AnswerMean$=\frac{\sum x}{ N } $
$=\frac{148+162+160+154+170+162+x+152}{8} $
$=\frac{1108+x}{8} $
$\therefore 158=\frac{1108+x}{8} $
$\Rightarrow 1264=1108+ x $
$\Rightarrow x=156$
$\therefore$ Mean height $=156 \ cm$.
View full question & answer→Question 33 Marks
The marks obtained by $10$ students are listed below:$2, 5, 3, 8, 0, 9, x, 6, 1, 8.$If the mean marks is $5,$ find $x.$
AnswerMean $=\frac{\sum x}{N} $
$=\frac{2+5+3+8+0+9+x+6+1+8}{10} $
$ =\frac{42+x}{10} $
$ \therefore 5=\frac{42+x}{10} $
$ \Rightarrow 50=42+x $
$ \Rightarrow x=50-42=8 .$
View full question & answer→Question 43 Marks
The daily maximum relative humidity $($in percent$)$ in Mumbai from May $1$ to May $7, 1992$ is given below: $64, 70, 65, 80, 75, 78.$Find the mean.
AnswerData: $64,70,65,80,75,78$
Total number of observation $=n=6$
Mean $=\frac{\text { Sum of observations }}{\text { Total number of observations }} $
$=\frac{64+70+65+80+75+78}{6} $
$=72 .$
View full question & answer→Question 53 Marks
A boy scored the following marks in various class tests during a term, each test being marked out of $20.15, 17, 16, 7, 10, 12, 14, 16, 19, 12, 16.$What is his median marks?
AnswerArranging the given marks in ascending order, $7,10,12,12,14,15,16,16,16,17,19$
Here $N =11$
$\therefore$ Median is $\left(\frac{ N +1}{2}\right)^{\text {th }}$ term
$=\left(\frac{11+1}{2}\right) $
$=6^{\text {th }}$ term
$\therefore$ Median marks $=15$.
View full question & answer→Question 63 Marks
A boy scored the following marks in various class tests during a term, each test being marked out of $20.15, 17, 16, 7, 10, 12, 14, 16, 19, 12, 16.$What is his mean marks?
AnswerTotal marks scored by the boy in $11$ tests
$=15+17+16+7+10+12+14+16+19+12+16 $
$=154 $
$\therefore$ Mean marks
$=\frac{154}{11} $
$=14 .$
View full question & answer→Question 73 Marks
The mean of $200$ observations is $20.$ It is found that the value of $180$ is wrongly copied as $280.$ Find the actual mean.
AnswerSince mean of $200$ observations $=20$
$\Rightarrow$ Sum of $200$ observations
$=200 \times 20$
$=4000$
$\Rightarrow$ Incorrect sum $=4000$
$\therefore$ Correct sum
$=$ Incorrect sum $-$ Incorrect value $+$ Correct value
$=4000-280+180$
$=3900$
$\therefore$ Correct mean
$=\frac{\text { Correct sum }}{3900}$
$=\frac{200}{20.5}$
$=19.5$
View full question & answer→Question 83 Marks
The mean monthly income of $8$ men is $Rs. 8079.75.$ A man whose monthly income is $Rs. 8280$ has also been taken into consideration. Calculate the mean monthly income of all the men.
AnswerSince mean monthly income of 8 men $= Rs. 8079.75$
$ \Rightarrow$ Sum of income of $8$ men
$=8 \times 8079.75$
$= Rs.64638 $
By considering one income of $Rs. 8280 ,$
Total number of men $=9$
Sum of income of $9$ men of all men
$ =\text { Rs. }(64638+8280)$
$=\text { Rs. } 72918$
$\therefore$ Mean monthly income of all men
$=\frac{72918}{8}$
$=\text { Rs. } 8102 . $
View full question & answer→Question 93 Marks
The mean of $4$ observations is $20.$ If one observation is excluded, the mean of the remaining observations becomes $15.$ Find the excluded observation.
AnswerSince mean of $4$ observation $= 20$
$\Rightarrow $ Sum of $4$ observation
$= 4 \times 20$
$= 80$
By excluding one observation,
the mean of the remaining $3$ observations $= 15$
$\Rightarrow $ Sum of remaining $3$ observation
$= 3 \times 15$
$= 45$
$\therefore $ Excluded observation
$=$ Sum of 4 observation $-$ Sum of $3$ observations
$= 80 - 45$
$= 35.$
View full question & answer→Question 103 Marks
The mean of $16$ natural numbers is $48.$ Find the resulting mean, if each of the number is decreased by $10\%$
AnswerMean $= 48$
Total numbers $= n = 16$
Therefore,
Resulting mean $($when each number is decreased by $10\%)$
$= 48 - 10\% = 48$
$= 48 - 4.8$
$= 43.2.$
View full question & answer→Question 113 Marks
The mean of $16$ natural numbers is $48.$ Find the resulting mean, if each of the number is increased by $50\%$
AnswerMean $= 48$
Total numbers $= n = 16$
Therefore,
Resulting mean $($when each number is increased by $50\%)$
$= 48 + 50\% of 48$
$= 48 + 24$
$= 72.$
View full question & answer→Question 123 Marks
The mean of $16$ natural numbers is $48.$ Find the resulting mean, if each of the number is divided by $0.25$
AnswerMean $= 48$
Total numbers $= n = 16$
Therefore,
Resulting mean $($when each number is divided by $0.25) = 48 + 0.25$
$= 192.$
View full question & answer→Question 133 Marks
In History project, marks out of $20$ were awarded to $8$ students. The marks were as shown below $: 14, 16, 18, 14, 16, 14, 12, 16$Each of the above students was $2$ extra marks for submitting the project a week before the due date. What is the revised mean of this group?
AnswerWhen extra $2$ marks are awarded, new addition to total marks scored
$=2 \times 8 $
$=6$
$\therefore$ New total marks scored
$=120+16$
$=136$
$\therefore$ Revised mean marks
$=\frac{136}{8} $
$=17 .$
View full question & answer→Question 143 Marks
In History project, marks out of $20$ were awarded to $8$ students. The marks were as shown below:$14, 16, 18, 14, 16, 14, 12, 16:$Find the mean marks.
AnswerTotal marks awarded to $8$ students
$=14+16+18+14+16+14+12+1 $
$=120$
Mean marks
$=\frac{120}{8} $
$=15 .$
View full question & answer→Question 153 Marks
Explain the meaning of the following terms: True Class Limits
AnswerTrue Class limits: When we group a number of variates together then the lowest value of the variate and the highest value of the variate form the class limits.
Let the class intervals for some grouped data be $10 - 20, 20 - 30, 30 - 40$ etc.
This is an exclusive frequency distribution.
For the class $20 - 30, 20$ is the lower limit, while $30$ is the upper limit.
Here the limits are actual and are called true class limits.
View full question & answer→