### Video Transcript

The table shows information about
the lengths of time 30 actors spent in hair and makeup. So we have Time, 𝑡 minutes and
Frequency. If 𝑡 is greater than or equal to
zero, but less than 10, the frequency is five. If 𝑡 is greater than or equal to
10, but less than 15, the frequency is eight. If 𝑡 is greater than or equal to
15, but less than 30, the frequency is 12. If 𝑡 is greater than or equal to
30, but less than 35, the frequency is three. And if 𝑡 is greater than or equal
to 35, but less than 60, the frequency is two. Alina drew a histogram for this
information. Write down two mistakes she has
made.

To know which is the first mistake
that Alina has made, what we’re gonna do is actually to have a look at the
graph. And we can see that actually the
𝑦-axis we have Frequency density, which is correct because if we’re drawing a
histogram, we want the frequency density to be on the 𝑦-axis.

However, if we look at the table,
there is no indication that she’s actually worked out the frequency density because
we haven’t got a column, where it would have frequency density and this has been
calculated, or class width, or anything like this. So this would immediately make us
think, “Hold on, is there an error here?”

So let’s have a look at what’s
actually has been plotted on the graph. Well, if we look between zero and
10, we can see that actually it has been plotted at five. Well, that’s in fact the frequency,
not the frequency density. Hold on! let’s see if this is the
case as we go along. Well, yes, if we actually look at
the next bar or next column, we can see that this is actually eight, which again is
the frequency. And if we continue across the
histogram, we can see that actually this is the case all along.

So what has actually happened is
the frequency has been plotted instead of the frequency density. Now, that’s the first mistake we’ve
actually spotted because we can say that she has plotted frequency and not the
frequency density. Okay, what’s her second
mistake?

Well, if we’re looking for a second
mistake, what we can see is that there are actually in fact gaps between each of our
bars. And we can actually say that well,
this is a mistake because on a histogram, you should not have gaps between the class
intervals. That would actually be in fact what
you’d have in a bar chart.

So therefore, we can say that the
second mistake that she has made is that there are gaps between the bars, which
should not be there. And like I said, if there are gaps
between the bars, that’s what you’d have in a bar chart, not a histogram.

So therefore, we have actually
completed the question because the question asked us to write down two mistakes that
Alina had made when she actually drew a histogram for the information given in the
table. And we said the first mistake was
that she plotted frequency and not the frequency density. This is a very common mistake. So watch out for this. And the second part there are gaps
between the bars, which should not be there, because gaps are not on histograms, but
you will find them on bar charts.