draw a box plot for the following data. {14, 27, 12, 16, 22, 20, 16, 25, 24, 15, 28, 21, 23, 21, 28}

Explanation:

Step1: Sort the data

$12, 14, 15, 16, 16, 20, 21, 21, 22, 23, 24, 25, 27, 28$

Step2: Find the median (Q2)

There are 14 data - points. The median is the average of the 7th and 8th ordered values. $\frac{21 + 21}{2}=21$.

Step3: Find the lower half of the data

The lower half is $12, 14, 15, 16, 16, 20, 21$. The median of the lower half (Q1) is 16.

Step4: Find the upper half of the data

The upper half is $21, 22, 23, 24, 25, 27, 28$. The median of the upper half (Q3) is 24.

Step5: Find the minimum and maximum

The minimum value is 12 and the maximum value is 28.

Step6: Analyze box - plot characteristics

The box in the box - plot has the left - hand side at Q1 = 16, the line inside the box at Q2 = 21, the right - hand side of the box at Q3 = 24. The whiskers extend from the box to the minimum (12) and maximum (28) values.

Answer:

We need to visually check which box - plot has the left end of the box at 16, the middle line at 21, the right end of the box at 24, and whiskers extending to 12 and 28. Without seeing the full details of the box - plots in the options, if we assume the correct construction based on the above calculations, we can determine the correct one. But if we assume the standard construction of box - plots with the described values, we can analyze the intervals. The box should start at 16, have a middle line at 21 and end at 24 with whiskers to 12 and 28. If we had to make a choice based on the values we calculated, we would look for a box - plot with these key features. Since we don't have the full visual details of the options in a way that can be precisely compared, we assume the correct box - plot has these characteristics. If we assume the options are constructed correctly, we note that the box should span from 16 to 24 with a line at 21 and whiskers to 12 and 28.