2 Marks Questions

Question 12 Marks

Find the mean of first six multiples of $4.$

Answer

First six multiples of $4$ are $4, 8, 12, 16, 20, 24.$
$\text{Mean}=\frac{\text{Sum of all observations}}{\text{Total number of observations}}$
$=\frac{4+8+12+16+20+24}{6}$
$=\frac{84}{6}=14$
Hence, the mean of first six multiples of $4$ is $14.$

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Question 22 Marks

The marks in a subject for $12$ students are as follows: $31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29$ For the given data, find the: Mean.

Answer

Given data is $31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29.$
Rearranging the given data in ascending order, $17, 18, 23, 25, 29, 31, 35, 35, 35, 37, 38, 42$
$\text{Mean}=\frac{\text{Sum of all observation}}{\text{Total number of observations}}$
$=\frac{17+18+23+25+29+31+35+35+35+37+38+42}{12}$
$=\frac{365}{12}=30.41$

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Question 32 Marks

The marks in a subject for $12$ students are as follows: $31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29$ For the given data, find the: Median.

Answer

Given data is 3$1, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29.$
Rearranging the given data in ascending order, $17, 18, 23, 25, 29, 31, 35, 35, 35, 37, 38, 42$
Here, $n = 12($even$)$
$\text{Median}=\frac{\text{Value of}\Big(\frac{\text{n}}{2}\Big)\text{th observation + Value of}\Big(\frac{\text{n}}{2}\Big)\text{th observation}}{2}$
$=\frac{\text{Value of 6th observation + Value of 7th observation}}{2}$
$=\frac{31+35}{2}=\frac{66}{2}=33$

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Question 42 Marks

Given below are heights of $15$ boys of a class measured in cm: $128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154.$
Find:
The median height of the boy.

Answer

Given, height (data) of $15$ boys of a class are: $128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154.$
Arranging the given data in ascending order, we have $128, 129, 136, 138, 140, 140, 142, 142, 143, 144, 144, 146, 150, 152, 154$
Here, $n = 15($odd$)$
$\therefore$ Median $=$ Value of $\Big(\frac{\text{n}+1}{2}\Big)\text{th}$ observation = Value of $\Big(\frac{15+1}{2}\Big)\text{th}$ observation
$=$ Value of 8th observation $= 142\ cm$

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Question 52 Marks

When a spinner with three colours given in figure is rotated, which colour has more chance to show up with arrow than the others?

Answer

From the figure, area covered by the yellow colour is maximum out of the given three colours. Hence, chances of yellow colour to show up with arrow will be more.

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Question 62 Marks

The letters written on paper slips of the word $MEDIAN$ and put in a bag. If one slip is drawn randomly, what is the probability that it bears the letter $D?$

Answer

In the word $‘ MEDIAN’,$ there is only one $D.$
So, favourable outcomes $=$ number of letter $D = 1$
Total number of possible outcomes $= 6$
$\therefore\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total number of possible outcomes}}$
$=\frac{1}{6}$

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Question 72 Marks

What is the probability that a student chosen at random out of $3$ girls and $4$ boys is a boy$?$

Answer

Given, total children $= 7$
$= 4$ boys and $3$ girls.
So, favourable outcomes for a day $= 4$
Total number of possible outcomes $= 7$
$\therefore\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total number of possible outcomes}}$
$=\frac{4}{7}$

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Question 82 Marks

Find the median of first nine even natural numbers.

Answer

First nine even natural numbers are $2, 4, 6, 8, 10, 12, 14, 16, 18$
Here, $n = 9($odd$)$
$\therefore$ Median $=$ Value of $\Big(\frac{\text{n}+1}{2}\Big)\text{th}$
observation $=$ Value of $\Big(\frac{9+1}{2}\Big)\text{th}$ observation
$=$ Value of 5th observation $= 10$
Hence, the median of first nine even natural numbers is $10.$

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Question 92 Marks

The following are weights (in kg) of $12$ people.
$70, 62, 54, 57, 62, 84, 75, 59, 62, 65, 78, 60$
Find the mean of the weights of the people.

Answer

The weights of $12$ persons are $70, 62, 54, 57, 62, 84, 75, 59, 62, 65, 78$ and $60.$
Sum of weights of $12$ people $= 70 + 62 + 54 + 57 + 62 + 84 + 75 + 59 + 62 + 65 + 78 + 60 = 788$
Number of observations $($persons$) = 12$
$\therefore\ \text{Mean}=\frac{\text{Sum of all observations (weight of 12 persons)}}{\text{Number of observations}}$
$=\frac{788}{12}=65.66$

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Question 102 Marks

Find the mean of the first ten even natural numbers.

Answer

First ten even natural numbers $= 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.$
Sum of all observations $= 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 110$
$\text{Mean}=\frac{\text{Sum of all observations}}{\text{Total observations}}$
$\therefore\ \text{Mean}=\frac{110}{10}=11$

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