Question

the data below represents the number of practices each member of nidhis ski team attended. 25, 28, 29, 29, 30, 34, 35, 35, 37, 38 which box plot correctly summarizes the data? choose 1 answer:

Explanation:

Step1: Find the minimum value

The minimum value in the data - set \(25,28,29,29,30,34,35,35,37,38\) is \(25\).

Step2: Find the first quartile (\(Q_1\))

The data - set has \(n = 10\) values. The lower half of the data is \(25,28,29,29,30\). The median of the lower half (\(Q_1\)) is the middle value of this sub - set. Since \(n = 5\) (odd), \(Q_1=29\).

Step3: Find the median (\(Q_2\))

Since \(n = 10\) (even), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered values. \(\frac{n}{2}=5\) and \(\frac{n}{2}+1 = 6\). The median \(Q_2=\frac{30 + 34}{2}=32\).

Step4: Find the third quartile (\(Q_3\))

The upper half of the data is \(34,35,35,37,38\). Since \(n = 5\) (odd), the median of the upper half (\(Q_3\)) is \(35\).

Step5: Find the maximum value

The maximum value in the data - set is \(38\).

A box - plot has a minimum value as the end of the left - most whisker, \(Q_1\) as the left side of the box, \(Q_2\) as the line inside the box, \(Q_3\) as the right side of the box, and the maximum value as the end of the right - most whisker.

Answer:

We need to check which box - plot has a minimum at \(25\), \(Q_1 = 29\), \(Q_2=32\), \(Q_3 = 35\), and a maximum at \(38\). Without seeing the other options, if option A has these values represented correctly on the box - plot (left whisker starts at \(25\), left side of the box at \(29\), line in the box at \(32\), right side of the box at \(35\), and right whisker ends at \(38\)), then the answer is A. Option Text (assuming option A has the correct values as described above). If there are other options, we would need to compare them based on these quartile and extreme values.