Video: Determining the Range and Interquartile Range of a Set Data Represented on Line Plot

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.

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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.

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