Men 2015 World Championships
Question 1
- Mean
Equation 1 shows the formula for calculating mean;
Equation 1
Where;
Rounding off to two decimal places;
- Median
Median is the middle value in a data set. To determine the median of ungrouped data, first, you have the arrange the data in ascending order. The learn the mean value.
The median for the time taken by the top 17 runners to complete 10,000 meters race in the 2015 World Championships is 1668.89 seconds.
- Range
Equation 2 shows the formula for calculating range.
Equation 2
- Standard deviation
Equation 3 shows the formula for calculating standard deviation of a sample;
Equation 3
Table 1
| 1621.13 | 1665.98 | -44.85 | 2011.522 |
| 1621.76 | 1665.98 | -44.22 | 1955.408 |
| 1622.83 | 1665.98 | -43.15 | 1861.923 |
| 1624.77 | 1665.98 | -41.21 | 1698.264 |
| 1628.91 | 1665.98 | -37.07 | 1374.185 |
| 1663.21 | 1665.98 | -2.77 | 7.6729 |
| 1663.69 | 1665.98 | -2.29 | 5.2441 |
| 1664.9 | 1665.98 | -1.08 | 1.1664 |
| 1668.89 | 1665.98 | 2.91 | 8.4681 |
| 1674.47 | 1665.98 | 8.49 | 72.0801 |
| 1687.5 | 1665.98 | 21.52 | 463.1104 |
| 1692.57 | 1665.98 | 26.59 | 707.0281 |
| 1694.72 | 1665.98 | 28.74 | 825.9876 |
| 1695.19 | 1665.98 | 29.21 | 853.2241 |
| 1696.3 | 1665.98 | 30.32 | 919.3024 |
| 1696.3 | 1665.98 | 30.32 | 919.3024 |
| 1704.47 | 1665.98 | 38.49 | 1481.48 |
Rounding off to two decimal places;
Women 2015 World Championships
- Mean
Use equation 1 to calculate the mean;
Rounding off to two decimal places;
- Median
Arrange the data set in ascending order then determine the middle value. In women’s category the median is 1913.01 seconds.
- Range
Using equation 2 to calculate range:
- Standard deviation
Table 2
| 1901.31 | 1917.92 | -16.61 | 275.8921 |
| 1901.77 | 1917.92 | -16.15 | 260.8225 |
| 1903.49 | 1917.92 | -14.43 | 208.2249 |
| 1903.58 | 1917.92 | -14.34 | 205.6356 |
| 1904.42 | 1917.92 | -13.5 | 182.25 |
| 1906.23 | 1917.92 | -11.69 | 136.6561 |
| 1909.73 | 1917.92 | -8.19 | 67.0761 |
| 1911.35 | 1917.92 | -6.57 | 43.1649 |
| 1913.01 | 1917.92 | -4.91 | 24.1081 |
| 1914.32 | 1917.92 | -3.6 | 12.96 |
| 1923.03 | 1917.92 | 5.11 | 26.1121 |
| 1926.14 | 1917.92 | 8.22 | 67.5684 |
| 1932.95 | 1917.92 | 15.03 | 225.9009 |
| 1935.26 | 1917.92 | 17.34 | 300.6756 |
| 1936.19 | 1917.92 | 18.27 | 333.7929 |
| 1940.87 | 1917.92 | 22.95 | 526.7025 |
| 1940.95 | 1917.92 | 23.03 | 530.3809 |
Using equation 3 to calculate standard deviation;
Rounding off to two decimal places;