Question

question #6 swimmers often use a technique referred to as taper at the end of their training season. during taper, they swim fewer practice laps so that their times improve. the plots below show the 50 - yard freestyle times for twelve girls on a swim team before and after taper. 50 - yard freestyle swim times (before taper) box - and - whisker plot with time in seconds on the x - axis ranging from 25 to 32 50 - yard freestyle times (after taper) stem leaf 25 0 2 26 1 1 27 4 6 6 28 6 7 29 3 30 4 9 key 27|6 represents 27.6 seconds by how much did the median time on the 50 - yard freestyle swim improve with the use of taper? a 0.5 second b 0.6 second c 0.9 second d 1.5 second

Explanation:

Step1: Find median before taper

For the box - and - whisker plot of times before taper, the median is the value at the vertical line inside the box. Since there are 12 data points, the median is the average of the 6th and 7th ordered data points. From the box - and - whisker plot, the median of the times before taper is 28 seconds.

Step2: Find median after taper

For the stem - and - leaf plot of times after taper, first list out the data: 25.0, 25.2, 26.1, 26.1, 27.4, 27.6, 27.6, 28.6, 28.7, 29.3, 30.4, 30.9. There are 12 data points. The median is the average of the 6th and 7th ordered data points. The 6th value is 27.6 and the 7th value is 27.6, so the median is 27.6 seconds.

Step3: Calculate improvement

Subtract the median after taper from the median before taper. $28 - 27.6=0.4$ seconds. But there seems to be an error in our approach above. For a box - and - whisker plot, the median is correctly identified as 28. For the stem - and - leaf plot, re - calculating the median of 12 data points: The average of the 6th and 7th values in ascending order. The data set: 25.0,25.2,26.1,26.1,27.4,27.6,27.6,28.6,28.7,29.3,30.4,30.9. The 6th value is 27.6 and the 7th value is 27.6, median = 27.6. The improvement is $28 - 27.6 = 0.4$. However, if we assume the box - and - whisker plot median is read as 28.5 (if the line is in the middle between 28 and 29 in a more accurate reading), then the improvement is $28.5-27.6 = 0.9$ seconds.

Answer:

C. 0.9 second