A group of adults were asked
how many children they
have in their families.
The bar graph below shows
the number of adults
who indicated each number of children.
So notice how we have the responses,
the number of children
along the horizontal axis
and the frequency of that
response along the vertical axis.
Notice how three responded
they have zero children.
Six responded they have one child.
Five responded they have two children.
Two responded they have three children.
One responded they have four children
and two responded they have five children.
We're first asked how many
adults were questioned.
This would be the sum of the frequencies
which in this case would be three plus six
plus five plus two plus one plus two
which equals 19.
So now we know 19 adults were questioned.
Next we're asked what percent
of adults questioned had five children.
So in looking at the bar graph again
notice how two adults responded
they have five children.
So because two out of 19 responded
they have five children,
the fraction of adults
that had five children
would be two-nineteenths.
Now that we know the fraction of adults
that had five children, we
can convert this fraction
to a percentage to answer this question.
You can also solve this a second way
using a percent proportion.
But to convert a fraction to a percent
we first convert to a decimal by dividing
and then we convert the
decimal to a percent.
To convert the fraction to a decimal
we want to divide two by 19.
So using the calculator notice that two
divided by 19, if you round
to three decimal places
will be approximately
zero point one zero five.
Now to convert to a
percentage we multiply by 100
and add a percent sign which is equivalent
to moving a decimal point
to the right two places
and adding a percent sign.
So notice how either way we get a percent
which would be approximately 10.5%.
So if we round to one decimal place
again our answer would be 10.5%.
The percent sign is already here
so we just enter 10.5.
So this would be one way
to answer this question.
Let's also set this up
as a percent proportion.
Remember a percent is a
number compared to 100.
So as a proportion which is where we have
two rates or ratios equal to each other.
If two out of the sample of
19 said they had 5 children
then two is to 19 as
what number is to 100,
so we'll say p is to 100.
So this number here p compared to 100
would be the percent of adults
that responded they had five children.
So to solve this proportion we would
cross multiply and solve for p.
So we'd have 19 times p
must equal two times 100.
So 19 p is equal to two times 100 is 200
dividing both sides by 19 ...
Let's go back to the calculator.
200 divided by 19 ...
notice is approximately 10.5.
10.5 over 100 is equal to 10.5%.
Now we could also solve this
using a percent equation
but I think the two methods
that we discussed here
are probably the most intuitive.
I hope you found this helpful.
