cora got a new pedometer. it keeps track of how many steps she walks each day. steps walked 7,773 8,454…

Explanation:

Step1: Arrange data in ascending order

$5,500,6,684,7,316,7,773,8,227,8,454,8,546,9,000$

Step2: Find the minimum value

The minimum value is $5,500$.

Step3: Find the first - quartile ($Q_1$)

There are $n = 8$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{8+1}{4}=2.25$. So $Q_1=6,684+(7,316 - 6,684)\times0.25=6,684 + 158=6,842$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n+1}{2}=\frac{8 + 1}{2}=4.5$. So $Q_2=\frac{7,773+8,227}{2}=8,000$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(8 + 1)}{4}=6.75$. So $Q_3=8,454+(8,546 - 8,454)\times0.75=8,454+69=8,523$.

Step6: Find the maximum value

The maximum value is $9,000$.

The box - plot should have the left - most whisker starting at $5,500$, the left side of the box at $Q_1\approx6,842$, the line inside the box at $Q_2 = 8,000$, the right side of the box at $Q_3\approx8,523$ and the right - most whisker ending at $9,000$. By comparing the two given box - plots with these values, we can determine the correct one.

Answer:

We need to visually compare the calculated values of minimum, $Q_1$, $Q_2$, $Q_3$ and maximum with the two box - plots provided. Without explicitly showing the two box - plots side - by - side with the calculated values marked, assume we have made the visual comparison and found the correct box - plot. If the first box - plot has the whisker starting at around $5,500$, box starting around $6,842$, middle line at $8,000$, box ending around $8,523$ and whisker ending at $9,000$, then the answer is the first box - plot. If the second box - plot has these characteristics, then the answer is the second box - plot. (Since the visual comparison of the actual box - plots is not fully possible in text, the above is the general way to determine the answer).