Question

Assume the following data represent the cost of a gallon of gasoline ($) at all the various gas stations around town on a given day. Take a random sample of size 5 from this population.

2.59 3.01 3.15 2.83 2.79 2.59 2.96 3.05 3.19 3.03 2.65 2.74 2.83 2.69 3.05 3.10 2.89 2.84 2.63 3.11 2.76 2.89 2.90 3.09 3.05 2.71 2.84 2.90 2.75 2.90 2.56 2.89 2.76 2.87 2.92 3.05 3.09 2.57 3.20 2.76

a) Describe the individual, variable, population and sample.

b) A description of the process you went through to actually collect the random sample.

c) The work showing the calculation of the mean and standard deviation by hand. (You may use a basic calculator for the arithmetic.)

d) A sentence explaining the meaning of the standard deviation in terms of the gasoline prices.

Answer 1

a)

Individual- Individual means one single quantity which represent the cost of a gallon of gasoline.

Variable - A variable is any characteristics, number or quantity that can be measured or counted and whose value vary.

Population- Population is a group of set of similar items or event of interest.

Sample - sample is a part of population.

b)

Simple Random Sampling without replacement (SRSWOR)- In this method once sample is selected it wont be replaced in the population and another sample is selected then it also wont replace in the population. Process is continued till desired number of sample size is selected. for this process we use computer to select the desired sample.

c)

Mean = sum(xi) / n

   = (3.09 +3.20 +2.84 +2.76 +2.83 +3.10 +2.76+ 2.76 +2.56+ 2.89) / 10

Mean= 2.879

d ) The meaning of the standard deviation in terms of the gasoline prices is it is a actual variation or deviation of the data from its mean or average value.

See following attachments to see selection of random sample described in part b using R software,