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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.

Respuesta :

Answer:

The sample mean is [tex]\bar{x}=1.24[/tex] and the sample median is 0.56

Step-by-step explanation:

The sample mean [tex]\bar{x}[/tex] of observations [tex]x_1,x_2,...,x_n[/tex] is given by

[tex]\bar{x}=\frac{\sum x_i}{n}[/tex]

Applying the above definition we get that

The sum of these 15 sample observations is

[tex]\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[/tex]

and the sample mean is

[tex]\bar{x}=\frac{18.6}{15}=1.24[/tex]

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 = [tex](\frac{n+1}{2} )^{th}[/tex]

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

Applying the above definition we get that

The data is already ordered and n = 15 so,

Sample median =  [tex](\frac{15+1}{2} )^{th}=8^{th}[/tex] = 0.56

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