The histogram below shows
information about the number of words per article written by a new local
newspaper. The newspaper has written 1065
articles in total. 15 percent of the articles between
200 and 350 words are written in the technology section of the newspaper. Work out an estimate for the number
of technology articles between 200 and 350 words.
In a histogram, the area of each
bar represents its frequency. Each bar is a rectangle. So the frequency can be found by
multiplying its width by its height or its frequency density. Let’s start then by finding the
total frequency of the articles with between 200 and 350 words.
We will need to do this in two
parts by first considering the number of articles with between 200 and 300 words,
represented by this shaded bar. Remember the frequency is given by
the area of each bar. Its width is 100 and its height is
3.4. We can interpret this scale by
recognising that 10 little squares is equal to one on the frequency density
scale. This means that one little square
must be equal to 0.1. The top of the bar sits four little
squares above the number three, which means it must have a height of 3.4. This means that there are 340
articles with between 200 and 300 words.
Next, we need to calculate the
number of articles with between 300 and 350 words. That’s just a portion of this
larger bar. The width of the bar shaded is
50. And once again, using a scale that
one little square is equal to 0.1, we can see that the height of this bar is
1.6. There are, therefore, 80 articles
with between 300 and 350 words.
Adding these two numbers together,
we can see the total number of articles with between 200 and 350 words is 420. We are told that 15 percent of
these articles are written in the technology section. We, therefore, need to find 15
percent of 420. There are a number of different
ways we can perform this calculation. If we were in a noncalculator
paper, we could start by finding 10 percent of 420 by dividing by 10. This gives us 42. Next, we halve this number to get
five percent of 420 is equal to 21. Adding these together gives us 15
percent of 420 is equal to 63.
Alternatively, we know that percent
means out of 100. So we could work out 15 divided by
100 multiplied by 420 or we could even convert 15 out of 100 into a 0.15. Each of these calculations will
give you the exact same answer.
An estimate for the number of
technology articles between 200 and 350 words is, therefore, 63.