water supply is deemed contaminated if metal in water is larger than 0.5 g L-1. 6 tests at different locations of the same water supply can be shown in the table. Location 1 2 3 4 5 6 Concentration (g L-1) 0.43 0.64 0.59 0.54 0.73 0.49 i) calculate mean concentration and standard deviation of the data ii) using an appropriate statistical test, show what evidence (if any) there is to suggest the water supply is contaminated.
water supply is deemed contaminated if metal in water is larger than 0.5 g L-1. 6 tests at different locations of the same water supply can be shown in the table. Location 1 2 3 4 5 6 Concentration (g L-1) 0.43 0.64 0.59 0.54 0.73 0.49 i) calculate mean concentration and standard deviation of the data ii) using an appropriate statistical test, show what evidence (if any) there is to suggest the water supply is contaminated.
water supply is deemed contaminated if metal in water is larger than 0.5 g L-1. 6 tests at different locations of the same water supply can be shown in the table. Location 1 2 3 4 5 6 Concentration (g L-1) 0.43 0.64 0.59 0.54 0.73 0.49 i) calculate mean concentration and standard deviation of the data ii) using an appropriate statistical test, show what evidence (if any) there is to suggest the water supply is contaminated.
water supply is deemed contaminated if metal in water is larger than 0.5 g L-1. 6 tests at different locations of the same water supply can be shown in the table.
Location
1
2
3
4
5
6
Concentration (g L-1)
0.43
0.64
0.59
0.54
0.73
0.49
i) calculate mean concentration and standard deviation of the data
ii) using an appropriate statistical test, show what evidence (if any) there is to suggest the water supply is contaminated.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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