Find the standard deviation for each data set. Use the standard deviations to compare the pair of data sets.
fastest recorded speeds of various large wild cats (miles per hour):
70 55 40 35 45 30 25 45 25
fasted recorded speeds of various birds in flight (miles per hour):
216 105 92 54 65 35 55 30 50 25 25 20
The standard deviation of the large wild cats is a
(Round the final answer to the nearest hundredth as needed. Round all intermediate values to the nearest hundredth as needed.)
The standard deviation of the birds in flight is a
(Round the final answer to the nearest hundredth as needed. Round all intermediate values to the nearest hundredth as needed.)
The standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate
speeds of birds in flight.
^
less
more
from the mean than the fastest recorded

standard deviation of the large wild cats is approximately 12.5. This value is calculated by finding the difference between each data point and the mean, squaring that difference, summing up those squared differences, dividing by the total number of data points minus one, and then taking the square root of that result. In this case, the mean of the large wild cats’ speeds is around 43.5 miles per hour. So, we calculate:

[(70-43.5)² + (55-43.5)² + … + (25-43.5)²] / (9 - 1) = 1246.875 / 8 = 155.86125 Square root of 155.86125 = approximately 12.5

The standard deviation of the birds in flight is approximately 37. Similar to the wild cats’ calculation, we find the mean of this data set to be around 78 miles per hour. Then we calculate:

[(216-78)² + (105-78)² + … + (20-78)²] / (12 - 1) = 99696 / 11 = 9063.273 Square root of 9063.273 = approximately 30 but since we need it in hundreds, it’s approximately 37

The standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate less from their mean than those of birds in flight. The smaller standard deviation for wild cats indicates that their recorded speeds are more clustered around their average value compared to birds in flight which have a larger spread or dispersion around their average speed.