2 Marks Questions

Question 12 Marks

In there is a histogram depicting daily wages of workers in a factory. Construct the frequency distribution table.

Answer

Class interval	Frequency
$150-200$ $200-250$ $250-300$ $300-350$ $350-400$	$50$ $30$ $35$ $20$ $10$
Total	$145$

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Question 22 Marks

The points scored by a basket ball team in a series of matches are as follows: $17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28$. Find the median and mode for the data.

Answer

Arranging the given data in ascending order, we get $2, 5, 7, 7, 8, 10, 10, 14, 17, 18, 24, 25, 27, 28, 48 $ We find, $10$ occurs most frequently i.e., maximum number of times. There, mode of the data $= 10$ Here, $n = 16$(even)

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Question 32 Marks

$30$ children were asked about the number of hours they watched $TV$ programmes last week. The results are recorded as under:

Number of hours	$0-5$	$5-10$	$10-15$	$15-20$
Frequency	$8$	$16$	$4$	$2$

Can we say that the number of children who watched $TV$ for $10$ or more hours a week is $22?$ Justify your answer.

Answer

$10$ is considered in $10 - 15$ and not in $5 - 10$. So, we cannot say that number of children who watched $TV$ for $10$ or more hours a week is $22$. In fact, the number of children who watch $TV$ for $10$ or more hours a week are $4 + 2 = 6.$

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Question 42 Marks

Mean of $50$ observations was found to be $80.4$. But later on, it was discovered that $96$ was misread as $69$ at one place. Find the correct mean.

Answer

Mean of 50 students of $= 80.4$
$\therefore$ Sum of observation $= 80.4 \times 50 = 4020$ As, $96$ was misread as $69$,
So, the correct total $= 4020 - 69 + 96 = 4047$
Hence, the correct mean $=\frac{4047}{50}=80.94$

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Question 52 Marks

In a diagnostic test in mathematics given to students, the following marks $($out of $100)$ are recorded: $46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44$ Which $'$average$’$ will be a good representative of the above data and why?

Answer

Median will be a good representative of the data, because:
$i.$ Each value occurs once.
$ii.$ The data is influenced by extreme values.

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Question 62 Marks

The class marks of a continuous distribution are: $1.04, 1.14, 1.24, 1.34, 1.44, 1.54$ and $1.64$ Is it correct to say that the last interval will be $1.55 - 1.73$? Justify your answer.

Answer

It is not correct. Because the difference between two consecutive class marks should be equal to the class size. Here, difference between two consecutive marks is $0.1$ and class size of $1.55 - 1.73$ is $0.18$, which are not equal.

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