2 Marks Questions

Question 12 Marks

Use the bar graph to answer the question: How many students have dog as a pet?

Answer

It can be easily seen from the graph, that the bar of the dog is till $8$
Hence, $8$ students have dog as their pet.

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Question 22 Marks

Use the bar graph to answer the question: Which is the most popular pet?

Answer

As per the bar graph, it can be easily seen that the bar of the cat is the tallest
Hence, Cat is the most popular pet.

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Question 32 Marks

Find the mode and median of the data :$13, 16, 12, 14, 19, 12, 14, 13, 14.$

Answer

For Median. We arrange the data in ascending order, we get $12, 12, 13, 13, 14, 14, 14, 16, 19.$
Median is the middle observation.
Therefore, $14$ is the median
For Mode. Mode = observation with highest frequency $= 14.$

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Question 42 Marks

The scores in mathematics test (out of $25$) of $15$ students is as follows :$19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20$. Find the mode and median of this data. Are they same?

Answer

For Median. We arrange the data in ascending order, we get
$5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25$
Median is the middle observation.
Therefore, $20$ is the median.
For Mode. Mode = Observation with highest frequency $= 20$
Yes ! they are same.

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Question 52 Marks

The enrolment of a school during six consecutive years was as follows: $1555, 1670, 1750, 2013, 2540, 2820$. Find the mean enrolment of the school for this period.

Answer

Mean enrolment of the school for this period.
Mean = $\frac{\operatorname{sum} \text { of all observations }}{\text { numberof observations }}$
= $\frac{1555+1670+1750+2013+2540+2820}{6}$
= $\frac{12348}{6} = 2058$

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Question 62 Marks

Following table shows the points of each player scored in four games:

Player	Game $1$	Game $2$	Game $3$	Game $4$
$A$	$14$	$16$	$10$	$10$
$B$	$0$	$8$	$6$	$4$
$C$	$8$	$11$	Did not play	$13$

Now answer the following questions:
$i.$ Find the mean to determine $A\ ’s$ average number of points scored per game.
$ii.$ To find the mean number of points per game for $C$, would you divide the total points by $3$ or by $4?$ Why?
$iii.B$ played in all the four games. How would you find the mean?
$iv.$ Who is the best performer?

Answer

$i.$ As per the question, We have to find the mean of the points scored by $A$ to find its average
Now,
Scores of $A$ are $= 14, 16, 10, 10$
Hence, mean score$ =\frac{\text{Total runs scored by A}}{\text { Total number of games }} = \frac{14+16+10+10}{4} = \frac{50}{4}= 12.5$
Therefore, Mean score is $12.5.$
$ii.$ Here, we have to find the digit with which the total points of $C$ needs to be divided in order to find the mean number of points per game for $C.$
We know that,
Mean $ =\frac{\text { Sum of all observations }}{\text { Number of observations }}$
And,
We also know that $C$ played total of $3$ games
Hence,
The total points will be divided by $3$, in order to find the mean of the number of points per game for $C.$
$iii.$ As per the question,
We have to find the mean of the points scored by $B$ to find its average
Now,
Scores of $B$ are $= 0, 8, 6, 4$
Hence,
Mean score$ =\frac{\text { Total runs scored by } \mathrm{B}}{\text { Total number of games }} = \frac{0+6+8+4}{4} = \frac{18}{4} = 4.5$
Therefore, Mean score is $4.5.$
$iv.$ Here, we have to find the best performer among them.
We know that, the best performer will be the one who will have the greatest average among all.
Thus, we can observe that,
The best average among $A, B$, and $C$ is of $A$ that is $12.5$
Hence,
We can say that,
$A$ is the best performer among these three.

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Question 72 Marks

Find the median of the data: $24, 36, 46, 17, 18, 25, 35$

Answer

After arranging the data in ascending order, we get $17, 18, 24, 25, 35, 36, 46$
Median is the middle observation.
Therefore $25$ is the median.

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Question 82 Marks

Find the mode of the numbers: $2, 2, 2, 3, 3, 4, 5, 5, 5, 6, 6, 8$

Answer

Here, $2$ and $5$ both occur three times. Therefore, both of them are modes of the data.

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Question 92 Marks

A batsman scored the number of runs in six innings: $36, 35, 50, 46, 60, 55$
Calculate the mean runs scored by him in an inning.

Answer

Total runs scored in all the innings $= 36 + 35 + 50 + 46 + 60 + 55 = 282.$
To find the mean, we find the sum of all the observations and divide it by the number of observations.
Therefore, in this case,
mean =$\frac{282}{6}= 47$
Thus, the mean runs scored in an inning is $47.$

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