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SP7.4
Raina planted yellow and green squash in her vegetable garden. Then she recorded the length of each squash that she harvested.

Length of Yollow Squash
(cm)

8
10
16

8
12
14

18
20
6

Length of Green Squash (cm)

14
14
16

12
14
13

16
13
14

Make a box plot for each data set. Use the number lines provided below.
Which type of Raina's squash has a higher median length based on the box plots?
Based on the box plots, which type of Raina's squash would you infer has a more consistent length? Explain your reasoning.
Based on the box plots, which type of Raina's squash would you infer is generally shorter? Explain your reasoning.

SP $7$ . $4$ $\newline$ Raina planted yellow and green squash in her vegetable garden. Then she recorded the length of each squash that she harvested. $\newline$ \begin{tabular}{|c|c|c|} $\newline$ \hline \multicolumn{ $3$ }{|c|}{ Length of Yollow Squash $(\mathrm{cm})$ } \\ $\newline$ \hline $8$ & $10$ & $16$ \\ $\newline$ \hline $8$ & $12$ & $14$ \\ $\newline$ \hline $18$ & $20$ & $6$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ \begin{tabular}{|c|c|c|} $\newline$ \hline \multicolumn{ $3$ }{|c|}{ Length of Green Squash (cm) } \\ $\newline$ \hline $14$ & $14$ & $16$ \\ $\newline$ \hline $12$ & $14$ & $13$ \\ $\newline$ \hline $16$ & $13$ & $14$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ $1$ . Make a box plot for each data set. Use the number lines provided below. $\newline$ $2$ . Which type of Raina's squash has a higher median length based on the box plots? $\newline$ $3$ . Based on the box plots, which type of Raina's squash would you infer has a more consistent length? Explain your reasoning. $\newline$ $4$ . Based on the box plots, which type of Raina's squash would you infer is generally shorter? Explain your reasoning.

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Full solution

Q. SP

7

4

\newline

Raina planted yellow and green squash in her vegetable garden. Then she recorded the length of each squash that she harvested.

\newline

\begin{tabular}{|c|c|c|}

\newline

\hline \multicolumn{

3

}{|c|}{ Length of Yollow Squash

(\mathrm{cm})

} \\

\newline

\hline

8

10

16

\newline

\hline

8

12

14

\newline

\hline

18

20

6

\newline

\hline

\newline

\end{tabular}

\newline

\begin{tabular}{|c|c|c|}

\newline

\hline \multicolumn{

3

}{|c|}{ Length of Green Squash (cm) } \\

\newline

\hline

14

14

16

\newline

\hline

12

14

13

\newline

\hline

16

13

14

\newline

\hline

\newline

\end{tabular}

\newline

1

. Make a box plot for each data set. Use the number lines provided below.

\newline

2

. Which type of Raina's squash has a higher median length based on the box plots?

\newline

3

. Based on the box plots, which type of Raina's squash would you infer has a more consistent length? Explain your reasoning.

\newline

4

. Based on the box plots, which type of Raina's squash would you infer is generally shorter? Explain your reasoning.

Organize Yellow Squash Lengths: First, let's organize the lengths of the yellow squash in ascending order: $6, 8, 8, 10, 12, 14, 16, 18, 20$ .
Find Yellow Squash Median: Now, let's find the median for the yellow squash. Since there are $9$ data points, the median is the $5$ th number in the ordered list, which is $12$ cm.
Organize Green Squash Lengths: Next, let's organize the lengths of the green squash in ascending order: $12, 13, 13, 14, 14, 14, 14, 16, 16$ .
Find Green Squash Median: Now, let's find the median for the green squash. Since there are $9$ data points, the median is the $5$ th number in the ordered list, which is $14$ cm.
Compare Median Lengths: Based on the medians calculated, the green squash has a higher median length of $14\,\text{cm}$ compared to the yellow squash's median of $12\,\text{cm}$ .
Calculate Yellow Squash IQR: To determine consistency, we need to look at the interquartile range (IQR) for each type of squash. The IQR is the range between the first quartile ( $Q_1$ ) and the third quartile ( $Q_3$ ).
Calculate Green Squash IQR: For the yellow squash, $Q_1$ is the median of the first half of the data, which is $8$ , and $Q_3$ is the median of the second half of the data, which is $16$ . So, the IQR for yellow squash is $16 - 8 = 8$ cm.
Calculate Green Squash IQR: For the yellow squash, $Q_1$ is the median of the first half of the data, which is $8$ , and $Q_3$ is the median of the second half of the data, which is $16$ . So, the IQR for yellow squash is $16 - 8 = 8$ cm.For the green squash, $Q_1$ is the median of the first half of the data, which is $13$ , and $Q_3$ is the median of the second half of the data, which is $14$ . So, the IQR for green squash is $14 - 13 = 1$ cm.