Question

a data set lists the number of hours each student, from a chemistry class, studied for a final exam. for this data set, the minimum is 1, the median is 11, the third quartile is 12, the interquartile range is 4, and the maximum is 15. construct a box-and-whisker plot that shows the number of hours studied. begin by first placing the middle dot on the median. then work on placing the rest of the points starting with the ones closest to the median.

Answer 1

To create a box-and-whisker plot for the given data set, start by placing a dot on the median (11), draw a box from the first quartile (8) to the third quartile (12) and extend whiskers to the minimum (1) and maximum (15). There are no outliers as all values are within the acceptable range.

Step-by-step explanation:

To construct a box-and-whisker plot for a data set where the minimum number of hours studied is 1, median is 11, third quartile (Q3) is 12, interquartile range (IQR) is 4, and maximum is 15, follow these steps:

1. Draw a number line that includes all values from the minimum to the maximum.
2. Place a dot on the median value, 11.
3. Calculate the first quartile (Q1). Since we know Q3 is 12 and IQR is 4, we subtract 4 from 12 to get Q1, which is 8.
4. Draw a box from Q1 (8) to Q3 (12).
5. Extend a whisker from Q1 to the minimum value (1).
6. Extend another whisker from Q3 to the maximum value (15).
7. You now have a complete box-and-whisker plot.

There are no potential outliers in this data set because all values lie within the range determined by Q1 - 1.5(IQR) and Q3 + 1.5(IQR).