Question

A team of professional runners are training for the 100-meter dash. On a given day of training, the following best times of the day (in seconds) have been recorded for 16 runners:

10.15 11.12 10.17 10.35 11.09 10.69 10.00 11.09 10.45 10.85 10.42 11.20 10.90 9.92 11.58 11.48

1. Compute sample mean and sample standard deviation.

2. Compute median, lower and upper quartiles, and interquartile range.

3. Two new athletes joined the team during the training session and ran with a personal daily

   best of 10.10 and 11.27 seconds, respectively. Show and discuss why the median time will be unchanged after adding these new data points to the data.

Answer 1

Compute sample mean and sample standard deviation
Compute median, lower and upper quartiles, and interquartile range.

Two new athletes joined the team during the training session and ran with a personal daily

best of 10.10 and 11.27 seconds, respectively. Show and discuss why the median time will be unchanged after adding these new data points to the data.

Initially there were 16 data point and hence the median was the average of the middle two values.
On adding two, there 18 data point and hence the median still remains the average of the middle two values.
The two new values have been added on either sides of the previous median as a highlight in above, hence the positon of the middle two values remain unchanged. Hence the median is the sam.e