Video: Pack 3 • Paper 1 • Question 22

Pack 3 • Paper 1 • Question 22

02:46

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.

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