Question

Mercury is a persistent and dispersive environmental contaminant found in many ecosystems around the world. When released as an industrial by-product, it often finds its way into aquatic systems where it can have deleterious effects on various avian and aquatic species. The accompanying data on blood mercury concentration (mu g/g) for adult females near contaminated rivers in a state was read from a graph in an article. 0.21 0.22 0.26 0.30 0.34 0.42 0.55 0.56 1.43 1.70 1.84 2.20 2.25 3.06 3.26 Determine the values of the sample mean and sample median.

Answer 1

Answer:

The sample mean is $\bar{x}=1.24$ and the sample median is 0.56

Step-by-step explanation:

The sample mean $\bar{x}$ of observations $x_1,x_2,...,x_n$ is given by

$\bar{x}=\frac{\sum x_i}{n}$

Applying the above definition we get that

The sum of these 15 sample observations is

$\sum x_i = 0.21+\:0.22+\:0.26+\:0.30+\:0.34+\:0.42\:+0.55+\:0.56+\:1.43+\:1.70+\:1.84+\:2.20+\:2.25+\:3.06+\:3.26\\\\\sum x_i =18.6$

and the sample mean is

$\bar{x}=\frac{18.6}{15}=1.24$

The sample median is obtained by first ordering the n observations from smallest to largest (with any repeated values included so that every sample observation appears in the ordered list). Then,

Sample median = The single middle value if n is odd = $(\frac{n+1}{2} )^{th}$

Sample median = The average of the two middle values if n is even = average of $(\frac{n}{2} )^{th}$ and $(\frac{n}{2}+1 )^{th}$

Applying the above definition we get that

The data is already ordered and n = 15 so,

Sample median =  $(\frac{15+1}{2} )^{th}=8^{th}$ = 0.56