Question

select the correct answer from each drop - down menu. the dot plot represents the scores of a group of students on an english test. if the dot plot is converted to a box plot, the first quartile would be drawn at, and the median would be drawn at.

Explanation:

Step1: Count the number of data - points

Count the total number of dots in the dot - plot. There are 1 + 2+3 + 2+1+1=10 data - points.

Step2: Calculate the position of the median

For a set of \(n = 10\) data - points, the median position is \(\frac{n + 1}{2}=\frac{10+1}{2}=5.5\). The median is the average of the 5th and 6th ordered data - points. Ordering the data: 2, 2, 3, 3, 4, 4, 4, 5, 5, 7. The 5th value is 4 and the 6th value is 4, so the median is 4.

Step3: Calculate the position of the first quartile

The first - quartile (\(Q_1\)) position for \(n = 10\) data - points is \(\frac{n + 1}{4}=\frac{10 + 1}{4}=2.75\). The first quartile is the value at the 2.75th position. Interpolating between the 2nd and 3rd ordered data - points. The 2nd value is 2 and the 3rd value is 3. \(Q_1=2+(3 - 2)\times0.75 = 2.75\approx3\).

Answer:

The first quartile would be drawn at 3, and the median would be drawn at 4.