Question

the list shows the number of math problems solved each week by a sixth - grade student. 23,19,26,21,31,16,21,29,27. which box plot best represents this list?

Explanation:

Step1: Arrange data in ascending order

$16,19,21,21,23,26,27,29,31$

Step2: Find the median (Q2)

There are 9 data - points. The median is the 5th value. So, Q2 = 23.

Step3: Find the lower half of data

The lower half is $16,19,21,21$. The median of the lower half (Q1) is $\frac{19 + 21}{2}=20$.

Step4: Find the upper half of data

The upper half is $26,27,29,31$. The median of the upper half (Q3) is $\frac{27+29}{2}=28$.

Step5: Identify the minimum and maximum

The minimum value is 16 and the maximum value is 31.

A box - plot has a box from Q1 to Q3 with a line at Q2, and whiskers from the minimum to Q1 and from Q3 to the maximum.

Answer:

The box - plot that has a minimum around 16, Q1 around 20, Q2 around 23, Q3 around 28, and a maximum around 31 is the correct one. Without seeing the exact visual details of the options, based on the calculated values, we can analyze the position of the box and whiskers. But if we assume the standard construction of box - plots, we need to look for a box - plot where the box starts around 20, has a line in the box around 23, ends around 28, and has whiskers extending to 16 and 31.