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Question

A box In Ms. Booth's class contains 200 loose white or yellow golf balls. The table below represents the results when 11 students each drew a random sample of the same number of balls, counted the number of yellows, and then returned the sample to the box.$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline \text{Student} & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {9} & {10} & {11} \\ \hline \text{Proportion of Yellow} & {0.6} & {0.7} & {0.3} & {0.7} & {0.5} & {0.9} & {0.8} & {0.8} & {0.7} & {0.7} & {0.9} \\ \hline \end{array}$Construct a box plot to display the data from Ms. Booth's class.

Solution

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A Box Plot is the visual representation of the statistical five-number summary of a given data set.

A five-number summary includes:

$\bullet$ Minimum

$\bullet$ First Quartile

$\bullet$ Median (Second Quartile)

$\bullet$ Third Quartile

$\bullet$ Maximum

$\textbf{Steps to create a box plot}$

$\textbf{Step 1:}$ Collect the data and organize the data from least to greatest.

The ascending order of the given data is $0.3$, $0.5$, $0.6$, $0.7$, $0.7$, $0.7$, $0.7$, $0.8$, $0.8$, $0.9$, $0.9$.

$\textbf{Step 2:}$ Find the median of the data set. The median is the middle number in an ordered data set.

For the given data $0.7$ is the number that's exactly in the middle, and therefore is our median. The median is also called the second quartile.

$\textbf{Step 3:}$ Find the first and third quartiles. The first quartile is the median of the lower half of the data set and the third quartile is the median of the upper half of the data set.

For the given data the lower half is $0.3$, $0.5$, $0.6$, $0.7$, $0.7$ and thus, the first quartile is $0.6$ and the upper half is $0.7$, $0.8$, $0.8$, $0.9$, $0.9$ and therefore the third quartile is $0.8$.

$\textbf{Step 4:}$ Draw the line long enough to hold all of your data and mark your first, second, and third quartiles on that line.

$\textbf{Step 5:}$ Make a box by drawing vertical lines connecting the quartiles and mark the outliers, minimum and maximum value and connect them to the box.

For the given data the minimum value is $0.3$ and the maximum value is $0.9$.

The required box plot of the given data is shown below.

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