Question

The dot plot represents a sampling of ACT scores: dot plot titled ACT Scores with Score on the x axis and Number of Students on the y axis with 1 dot over 18, 3 dots over 19, 4 dots over 21, 4 dots over 22, 3 dots over 23, 2 dots over 24, 1 dot over 25 Which box plot represents the dot plot data?

Answer 1

Step-by-step explanation:

Hi,

To draw a box plot, you require certain points on the graph calculated.

• Quartile 1
• Quartile 2 or Median
• Quartile 3

As per the information provided, your data looks like this:

(Each dot in the dot plot shows the frequency of the score)

18, 19, 19, 19, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 24, 24, 25.

Using the data, we first calculate the median.

Median of any data set is the most central value. Since there are 18 values in this data set, we consider the two most central values, which are the 9th and 10th values.

The 9th value of the data corresponds to 22.

The 10th value of the data corresponds to 22.

Hence the median is 22.

(Had these two values been different, we would have simply add them and divided the sum by 2 to find the median.)

Now we find Quartile 1, which is one-fourth value of the data.

$Q_{1} = \frac{n}{4} = \frac{18}{4} = 4.5$

4.5th value is Q1, which lies between 4th and 5th value.

4th value of the data set corresponds to 19.

5th value of the data set corresponds to 21.

We add them both and divide the sum by 2.

$\frac{19+21}{2} = 20$

Hence the first quartile is 20.

Now we find Quartile 3, which is three-fourth value of the data.

$Q_{3} = \frac{3n}{4} = \frac{18*3}{4} = 13.5$

13.5th value is Q3, which lies between 13th and 14th value.

13th value of the data set corresponds to 23.

14th value of the data set corresponds to 23.

Hence the third quartile is 23.

To plot the box, the top line of the box is at Q3, central line at Median and lower end of the box at Q1.

The two whiskers of the plot, upper is at the highest point: 25 and lower is at the lowest point: 18.

Your plot should look like this: