Question

The data of a certain number of people spending time watching T.V. is shown in the table given below. Select the option showing the correct line plot(s) for this data.

Time spent (h)

$\frac{1}{2}$

$\frac{3}{15}$

$\frac{1}{3}$

$\frac{1}{5}$

$\frac{10}{20}$

$\frac{3}{2}$

• A.
• B.
• C.

Answer 1

The correct option is A

Time taken (h)	Equivalent fraction
$\frac{1}{2}$	$\frac{1}{2}$
$\frac{3}{15}$	$\frac{3}{15}=\frac{3÷3}{15÷3}=\frac{1}{5}$
$\frac{1}{3}$	$\frac{1}{3}$
$\frac{1}{5}$	$\frac{1}{5}$
$\frac{10}{10}$	$\frac{10}{20}=\frac{10÷10}{20÷20}=\frac{1}{2}$
$\frac{3}{2}$	$\frac{3}{2}$

So, the markings on axis will be $\frac{1}{5},\frac{1}{3},\frac{1}{2}$ and $\frac{3}{2}$.
Convert the unlike fractions into the like fractions to arrange in ascending order to mark on the axis.

$\frac{1}{2}=\frac{1\times 15}{2\times 15}=\frac{15}{30}$

$\frac{1}{5}=\frac{1\times 6}{5\times 6}=\frac{6}{30}$

$\frac{1}{3}=\frac{1\times 10}{3\times 10}=\frac{10}{30}$

$\frac{3}{2}=\frac{3\times 15}{2\times 15}=\frac{45}{30}$

$\frac{6}{30}<\frac{10}{30}<\frac{15}{30}<\frac{45}{30}$

$\frac{1}{5}<\frac{1}{3}<\frac{1}{2}<\frac{3}{2}$

Now, the markings on the axis in ascending order will be
$\frac{1}{5},\frac{1}{3},\frac{1}{2}$ and $\frac{3}{2}$.

As shown on WB, options A and B are correct.