Question

In the 2000 Sydney Olympics, a special program initiated by IOC president Juan Antonio Samaranch allowed developing countries to send athletes to the Olympics without the usual qualifying procedure. Here are the 71 times for the first round of the 100 meter men’s swim (in seconds).60.39 49.93 53.40 51.82 50.46 51.36 50.28 50.19 52.1450.56 52.72 50.95 49.74 49.16 52.57 52.53 52.09 52.4049.75 54.06 53.50 50.63 51.93 51.62 52.58 53.55 51.0749.76 49.73 50.90 59.26 49.29 52.78 112.72 49.79 49.8352.43 51.28 52.22 49.76 49.70 52.90 50.19 54.33 62.4551.93 52.24 52.82 50.96 48.64 51.11 50.87 52.18 54.1250.49 49.84 52.91 52.52 50.32 51.52 52.00 52.85 52.2449.45 51.28 49.09 58.79 49.74 49.32 50.62 49.45Calculate the sample mean and sample standard deviation(use Excel functions).

Answer 1

The means for times for the first round of the 100 meter men’s swim is 52.64789 seconds

The satandar deviation for times for the first round of the 100 meter men’s swim is 7.60182 seconds

Explanation:

The sample mean for a set of n data is given by:

`\bar X = (1)/(n)\sum{x_i}`

In other words, the sample mean of the times for 71 times of the first round measured in seconds is:

`\bar X = (1)/(71)\sum{x_i} = 52.64789` seconds

The sample standard deviation for a set of n data is given by:

`S = \sqrt{(1)/(n-1)\sum{(x_i - \bar x)^2}}`

In other words, the sample standard deviation of the times for 71 times of the first round measured in seconds is:

`S = \sqrt{(1)/(n-1)\sum{(x_i - \bar x)^2}} = 7.60182` seconds