Study text: "Essential Mathematics and Statistics for Science", 2nd Edition,

G Currell & A A Dowman, Wiley-Blackwell, 2009

G Currell & A A Dowman, Wiley-Blackwell, 2009

- In a fish research programme, 501 trout are held in a tank.

The researcher wants to calculate a**single value**as a ‘**representative**’ weight (mass) for all of the fish.

Select**ALL**of the following methods that could calculate a suitable value for a ‘representative’ weight.

(Click here for the Video Answer) - Referring to the same 501 fish as in question 1, the weight (mass) of the first fish measured can be recorded as
*m*_{1}, the second as*m*_{2}, etc, up to*m*_{501}.

Select the**ONE**mathematical expression which describes the calculation of the mean value for the weight,*µ*:- None of the above

- Referring to the same 501 fish as in question 2, the owner wishes to save time, and only obtain an
**estimate**of the average weight of all the fish in the tank. He takes a random sample of 10 fish, calculates the mean weight of the 10 fish in his sample and uses this as an estimate for the true mean,*µ*, of the population of 501 fish.

(expressed as*m-bar*) would be used to describe the mean of a sample of values of '*m*'.

Select**ALL**of the following statements that are completely true

(Click here for the Video Answer) - Referring to the same 501 fish as in question 1, the mean weight of all the 501 fish is calculated as
*µ*. The owner wishes to calculate a*single value*to describe the**variations**in weight within the population of 501 fish.

The**deviation**in the weight of the*i*^{th}fish from the**mean value**is given as*d*=_{i}*m*-_{i}*µ*.

Select**ALL**of the following methods that would give a possible value for a**standard deviation**,*σ*, that could be used to describe the whole population.

(Click here for the Video Answer) - Referring to the same 501 fish as in question 4, the owner wishes to save time, but only obtain an
**estimate**of the standard deviation in the weights of all the fish in the tank. He first takes a random**sample**of 10 fish and calculates the mean weight, , of the 10 fish.

Select the**ONE**of the following equations for a sample standard deviation,*s*, that will then give the best**estimate**of the standard deviation,*σ*, of the weights of all the fish in the tank: - Referring to the same 501 fish as in question 5, assume that the number of fish taken as a sample measurement is
*n*.

Select**ALL**of the following statements that are completely true

(Click here for the Video Answer)