Final answer:
To create a box plot for the given data, you first arrange the data in order, then find the minimum, Q1, median, Q3, and maximum. These values are used to draw the plot, which displays the distribution, including any skewness.
Step-by-step explanation:
To summarize the data of the number of books twelve students have read with a box plot, we first need to identify several key statistics: the minimum, the first quartile (Q1), the median (second quartile, Q2), the third quartile (Q3), and the maximum.
- First, arrange the data in ascending order: 2, 4, 7, 8, 9, 12, 14, 18, 19, 21, 30, 32.
- Identify the minimum (2) and maximum (32) values.
- Find the median (Q2) which is the average of the 6th and 7th values: (12+14)/2 = 13.
- Find the first quartile (Q1) which is the median of the first half of the data: (4+7)/2 = 5.5.
- Find the third quartile (Q3) which is the median of the second half of the data: (19+21)/2 = 20.
The box plot is then drawn using these statistics, with a box extending from Q1 to Q3, a line within the box at Q2, and whiskers that extend from the minimum to Q1 and from Q3 to the maximum. The shape of the box plot can tell you about the distribution of the data such as whether it is skewed and where most of the data falls. In this case, the longer whisker towards the maximum indicates a right-skewed distribution, where there are more books read at the higher end than at the lower end.