Video Transcript
The given line plot shows the
magnitudes of the earthquakes that recently took place around the world. Determine the range and
interquartile range of the data.
One way of approaching this
question would be to write out all of the values in order, two, 2.1, 2.6, 2.6, 2.8,
and so on. This should be very time consuming,
so it is easier to work out how many earthquakes of each magnitude we have
first. There was one earthquake of
magnitude two. There was also one earthquake of
magnitude 2.1. There were two earthquakes of
magnitude 2.6, four of 2.8, all the way up to four of 3.5.
We can also calculate a running
total or cumulative frequency of these to calculate the total number of
earthquakes. This gives us values of one, two,
four, eight, 11, 15, 17, 21, 23, and 27. There were 27 earthquakes that took
place altogether. When dealing with a large data set,
we can calculate the position of the median and the quartiles as follows.
The median position can be
calculated by dividing 𝑛 plus one by two, where 𝑛 is the total number of data
values. In this question, we have 27 plus
one divided by two. This is equal to 14. So, the median is the 14th
number. Whilst we don’t need to calculate
the median in this case, it helps us work out the position of the quartiles. The 12th to 15th values all had a
magnitude of three. This means that the median equals
three.
The lower quartile or 𝑄 one
position will be half of this. As the seventh number is 2.8, the
lower quartile or 𝑄 one is 2.8. The upper quartile or 𝑄 three
position will be the 21st value. This means that 𝑄 three is equal
to 3.3. The range of values is calculated
by subtracting the minimum from the maximum. 3.5 minus two is equal to 1.5. So, this is the range. The interquartile range or IQR is
equal to 𝑄 three minus 𝑄 one. 3.3 minus 2.8 is 0.5. So, the interquartile range is
0.5.
