[2 Mark Question Answer]

Question 12 Marks

The mean of a certain number of observations is 32. Find the resulting mean, if the observation is, increased by 60%.

Answer

$ \text { Increased by }=60 \% $
Resulting mean $=32+60 \%$ of 32
$ \begin{aligned} & =32+\frac{60}{100} \times 32=32+\frac{192}{10} \\ & =\frac{32}{1}+\frac{19.2}{1}=51.2 \end{aligned} $

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Question 22 Marks

The mean of a certain number of observations is 32. Find the resulting mean, if the observation is, divided by 0.5

Answer

Observed mean $=32$
Divided by $=0.5$
$\therefore$ Resulting mean $=\frac{32}{0.5}=64$

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Question 32 Marks

The mean of a certain number of observations is 32. Find the resulting mean, if the observation is, multiplied by 2

Answer

Observed mean = 32
Multiplied by = 2
∴ Resulting mean = 32 × 2 = 64

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Question 42 Marks

The mean of a certain number of observations is 32. Find the resulting mean, if the observation is, decreased by 7

Answer

Observed mean = 32
Decreased by = 7
∴ Resulting mean = 32 − 7 = 25

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Question 52 Marks

The mean of a certain number of observations is 32. Find the resulting mean, if the observation is, increased by 3

Answer

Increased by = 3
Observed mean = 32
If increased by 3
∴ Resulting mean = 32 + 3 = 35

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Question 62 Marks

If different values of variable x are 19.8, 15.4, 13.7, 11.71, 11.8, 12.6, 12.8, 18.6, 20.5 and 2.1, find the mean.

Answer

$\begin{aligned} & 19.8+15.4+13.7+11.71+11.8+12.6+12.8+18.6+20.5+21.1 \\ & \therefore \text { Mean }=\frac{19.8+15.4+13.7+11.71+11.8+12.6+12.8+18.6+20.5+21.1}{10} \\ & =\frac{158.01}{10} \\ & =15.801\end{aligned}$

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Question 72 Marks

Find the mean of first ten odd natural numbers.

Answer

First ten odd natural numbers are $1,3,5,7,9,11,13,15,17,19$
$ \begin{aligned} & \therefore \text { Mean }=\frac{1+3+5+7+9+11+13+15+17+19}{10} \ldots . .(\text { Here } n=10) \\ & =\frac{100}{10} \\ & =10 \end{aligned} $

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Question 82 Marks

The birth rate per thousand of different countries over a particular period of time is shown below.

INDIA	U.K.	CHINA	GERMANY	SWEDEN
35	22	43	13	8

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Question 92 Marks

The following table shows the market positions of some brands of soap.
Draw a suitable bar graph:

Soap (brands):	A	B	C	D	E
No. of buyers:	51	27	15	24	18

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Question 102 Marks

Find the mode of 7, 7, 8, 10, 10, 11, 10, 13, 14

Answer

Arranging the numbers in ascending order = 7, 7, 8, 10, 10, 10, 11, 13, 14
Mostly repeated term =10
∴ Mode = 10

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Question 112 Marks

Find the mode of 5, 6, 9, 13, 6, 5, 6, 7, 6, 6, 3

Answer

Arranging the numbers in ascending order: 3, 5, 5, 6, 6, 6, 6, 6, 7, 9, 13
Mostly repeated term = 6
∴ Mode = 6

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Question 122 Marks

Mean of 5 numbers is 20 and the mean of the other 5 numbers is 30. Find the mean of all the 10 numbers taken together.

Answer

The mean of 5 number $=20$
Then, mean of other 5 number $=30$
$ \therefore \text { Mean }=\frac{20+30}{2}=\frac{50}{2}=25 $

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Question 132 Marks

Find the mean of first six natural numbers.

Answer

First six natural numbers are: $1,2,3,4,5,6$
$ \begin{aligned} & \therefore \text { Mean }=\frac{1+2+3+4+5+6}{6} \ldots . .(\text { Here } n=6) \\ & =\frac{21}{6} \\ & =3.5 \end{aligned} $

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Question 142 Marks

The rainfall (in mm) in a city on 7 days of a certain week is recorded as follows

Day:	Mon	Tue	Wed	Thus	Fri	Sat	Sun
Rainfall (in mm):	0.5	2.7	2.6	0.5	2	5.8	1.5

Find the total and average (mean) rainfall for the week.

Answer

The rainfall in a city on 7 days are $0.5,2.7,2.6,0.5,2,5.8,1.5$
Average rainfall $=\frac{0.5+2.7+2.6+0.5+2+5.8+1.5}{7}$ (Number of days $=7$ )
$ =\frac{15.6}{7} $
$ =2.2 \mathrm{~mm} $

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Question 152 Marks

Find the mean of the first six multiples of 5.

Answer

Six multiples of 5 are $5,10,15,20,25$ and 30
$ \begin{aligned} & \therefore \text { Mean }=\frac{5+10+15+20+25+30}{6} \ldots . .(\text { Here } n=6) \\ & =\frac{105}{6}=17.5 \end{aligned} $

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Question 162 Marks

Find the mean of first five prime numbers.

Answer

The first five prime numbers are $2,3,5,7,11$
$ \begin{aligned} & \therefore \text { Mean }=\frac{2+3+5+7+11}{5} \ldots \ldots \ldots . . .(\text { Here } n=5) \\ & =\frac{28}{5}=5 \frac{3}{5}=5.6 \end{aligned} $

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Question 172 Marks

Find the mean of first six multiples of 3.

Answer

The six multiples of 3 are $3,6,9,12,15,18$.
$ \begin{aligned} & \therefore \text { Mean }=\frac{3+6+9+12+15+18}{6} \ldots \ldots \ldots .(\text { Here } n=6) \\ & =\frac{63}{6} \\ & =10.5 \end{aligned} $

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Question 182 Marks

Find the mean of 53, 61, 60, 67 and 64.

Answer

Mean of 53, 61, 60, 67 and 64
$ \begin{aligned} & \therefore \text { Mean }=\frac{53+61+60+67+64}{5} \ldots . .(\text { Here } n=5) \\ & =\frac{305}{5} \\ & =61 \end{aligned} $

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Question 192 Marks

Arrange the following data in descending order:
3.3, 3.2, 3.1, 3.7, 3.6, 4.0, 3.5, 3.9, 3.8, 4.1, 3.5, 3.8, 3.7, 3.9 and 3.4.
How many numbers are 3.8 or above?

Answer

Descending order: 4.1, 4.0, 3.9, 3.9, 3.8, 3.8, 3.7, 3.7, 3.6, 3.5, 3.5, 3.4, 3.3, 3.2, 3.1 Number are 3.8 or above = 6
i.e., 3.8, 3.8, 3.9, 3.9, 4.0, 4.1

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Question 202 Marks

Arrange the following data in descending order:
3.3, 3.2, 3.1, 3.7, 3.6, 4.0, 3.5, 3.9, 3.8, 4.1, 3.5, 3.8, 3.7, 3.9 and 3.4.
How many numbers are less than 3.5?

Answer

Descending order: 4.1, 4.0, 3.9, 3.9, 3.8, 3.8, 3.7, 3.7, 3.6, 3.5, 3.5, 3.4, 3.3, 3.2, 3.1
Number less than 3.5 = 4
i.e., 3.4, 3.3, 3.2, 3.1

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