Question

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:

Construct a box plot of the data.

Short answer

The box plot of the given data is:

Step-by-step solution

To construct

The box plot for the given data.

Explanation

Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot.

Use a horizontal or vertical number line and a rectangular box to make a box plot. The axis's ends are labelled by the smallest and largest data values. One end of the box is marked by the first quartile, while the other end is marked by the third quartile. Approximately half of the data is included within the box. From the box's ends to the smallest and greatest data values, the "whiskers" extend. The median or second quartile can be in the middle of the first and third quartiles, or it can be either one or the other.

The box plot's five numerical summaries are as follows:

# of movies	Frequency	Cumulative frequency
0	5	5
1	9	14
2	6	20
3	4	24
4	1	25
	N=25

$$\begin{gathered} Minimum=0 \\ {Q}_1=\mathrm{size}of{\left(\frac{N+1}{4}\right)}^{\text{th}}item \\ =sizeof{\left(\frac{25+1}{4}\right)}^{\text{th}}item \\ =sizeof{6.5}^{\text{th}}item \\ =1 \end{gathered}$$

Median = size of${\left(\frac{N+1}{2}\right)}^{\text{th}}$item

= size of ${\left(\frac{25+1}{2}\right)}^{\text{th}}$item

= size of ${13}^{\text{th}}$item

= 1

$$\begin{gathered} Q_3=sizeof{\left(\frac{3(N+1)}{4}\right)}^{\text{th}} \\ {Q}_3=sizeof{\left(\frac{3(25+1)}{4}\right)}^{\text{th}}item \\ =sizeof{19.5}^{\text{th}} \\ =2 \end{gathered}$$

Maximum = 4

Hence the box of plot given data is: