The table shows the capacities of six sports stadiums around the world. Describe how the lower quartile will be affected if Emirates Stadium, London, United Kingdom, which has a capacity of 60,338, is included in the data.
In order to evaluate how the lower quartile has been affected, we need to calculate the lower quartile before the Emirates Stadium is added and after it is added. Let’s begin by looking at the initial values in the table. The smallest value in the table is 40,000. The next smallest is 42,055. Putting the six capacities in ascending order will allow us to calculate the median and then the lower quartile.
The median is the middle value. And, in this case, we have six capacities. This means that the median will be halfway between the third and fourth value. We could calculate this by finding the midpoint of 48,548 and 74,228. In this question, we’re only interested in the lower quartile. This involves the bottom half or lower half of the data, those values that are below the median. The lower quartile, or 𝑄 one, is the center of the bottom half. In this question, this will be the second value, 42,055. The lower quartile before the Emirates Stadium has been added is 42,055.
We will now consider what happens when we add this extra capacity. We now have seven values ranging from 40,000 to 86,047. The median or middle value now is 60,338. There are three values above this and three values below it. This means that the bottom half of capacities still contains three values. The middle or center of this will still be 42,055. This means that the lower quartile, once the Emirates Stadium has been added, is still 42,055. We can therefore conclude that the lower quartile will remain unchanged at 42,055.