Question

In the Northern Hemisphere, dolphins swim predominantly in a counterclockwise direction while sleeping. A group of researchers wanted to know whether the same was true for dolphins in the southern hemisphere. They watched 8 sleeping dolphins and found that they swam in a clockwise direction while sleeping the following percentages of time. Assume that this is a random sample and that this variable has a normal distribution in the population. Given the following observations of percentages of time spent swimming clockwise, the mean is (FILL IN THE BLANK)
and the median is (FILL IN THE BLANK)
Express your answers as percentages to one decimal place.

77.7, 84.8, 79.4, 84.0, 99.6, 93.6, 89.4, 97.2

Answer 1

Mean percentage = 88.57 %

Median  = 87.1

Solution:

Given that,

Given the following observations of percentages of time spent swimming clockwise

77.7, 84.8, 79.4, 84.0, 99.6, 93.6, 89.4, 97.2

Total observations = 8

Sum of observations = 77.7+ 84.8 + 79.4 + 84.0 + 99.6 + 93.6 + 89.4 + 97.2

Sum of observations = 705.7

Mean is given as:

$Mean = \frac{\text{sum of observations}}{\text{number of observations}}\\\\Mean = \frac{705.7}{8}\\\\Mean = 88.2125$

Mean percentage:

$Mean\ percentage = \frac{mean}{highest\ number} \times 100\\\\Mean\ percentage = \frac{88.2125}{99.6} \times 100\\\\Mean\ percentage = 88.57 \%$

Find median

Median is the middle value in data set

Arrange in ascending order

77.7, 79.4, 84.0, 84.8, 89.4, 93.6, 97.2, 99.6

$Median = \frac{84.8+89.4}{2}$

Median =  87.1