What are the first and third quartiles of the box and whisker plot above?
0 15 110 225
http://wme.cs.kent.edu/kimpton/img/boxwhisker.gif
To determine the first and third quartiles of a box and whisker plot, you need to know the values at the ends of the box. In this case, the lowest value is 0 and the highest value is 225.
The first quartile (Q1) is the median of the lower half of the data set. To find Q1, you divide the data set into two halves and find the median of the lower half. In this case, since there are four values, the lower half consists of the first two values: 0 and 15. To find the median of this lower half, you take the average of these two numbers: (0 + 15) / 2 = 7.5. So, the first quartile is 7.5.
The third quartile (Q3) is the median of the upper half of the data set. To find Q3, you divide the data set into two halves and find the median of the upper half. In this case, the upper half consists of the last two values: 110 and 225. To find the median of this upper half, you take the average of these two numbers: (110 + 225) / 2 = 167.5. So, the third quartile is 167.5.
Therefore, the first quartile is 7.5 and the third quartile is 167.5.