Q 3.20. - Elementary Statistics

Question

Find the 

a. Mean    b. median c. models 

For the mean and the median, round each answer to one more decimal place than that used for the observations. 

Hurricanes. An article by D. Schaefer et al. reported on a long-term study of the effects of hurricanes on tropical streams of the Luquillo Experinental Forest in Puerto Rico. The study shows that Hurricane Hugo had a significant impact on stream water chemistry. The following table shows a sample of $10$ammonia fluxes in the first year after Hugo. Data are in kilograms per hectare per year.

$96, 116, 66, 57, 147, 54, 147, 88, 175, 154$

Step-by-Step Solution

Answer

$$\begin{gathered} a) 120 \\ b) 131.5 \\ c) 147, 154 \end{gathered}$$

Step 1. Given information.

We have given data: $96, 116, 66, 57, 147, 54, 147, 88, 175, 154$.

Step 2. Mean of the data.

Mean$=\frac{Sum of observation }{Number of observation}$

$$\begin{gathered} =\frac{96+66+147+147+175+116+57+154+88+154}{10} \\ =\frac{1200}{10} \\ =120 \end{gathered}$$

Step 3. Median of the data.

Arrange the data in increasing order :$57, 66, 88, 96, 116, 147, 147, 154, 175$.

The number of observation is $10$.

The median is the mean of the  two  middle observation in the ordered list.

Median

$$\begin{gathered} =\frac{116+147}{2} \\ =\frac{263}{2} \\ =131.5 \end{gathered}$$

Step 4. Mode of the data.

The greatest frequency is the mode of the data set. 

Thus, the mode of the data set is $147, 154$.