Question 1 The following table shows the number of shirts by sizes that are manufactured in a factory on a particular week: Extra small Small Medium Large Extra Large 390 470 520 680 440 a) It was discovered that the sizing of some shirts was labelled incorrectly. (i) Give two reasons why it would be necessary to examine a sample of the shirts produced rather than examine the entire weekly production. (ii) State two differences between a cluster sample and a stratified random sample in this situation.
Question 1 The following table shows the number of shirts by sizes that are manufactured in a factory on a particular week: Extra small Small Medium Large Extra Large 390 470 520 680 440 a) It was discovered that the sizing of some shirts was labelled incorrectly. (i) Give two reasons why it would be necessary to examine a sample of the shirts produced rather than examine the entire weekly production. (ii) State two differences between a cluster sample and a stratified random sample in this situation.
Question 1 The following table shows the number of shirts by sizes that are manufactured in a factory on a particular week: Extra small Small Medium Large Extra Large 390 470 520 680 440 a) It was discovered that the sizing of some shirts was labelled incorrectly. (i) Give two reasons why it would be necessary to examine a sample of the shirts produced rather than examine the entire weekly production. (ii) State two differences between a cluster sample and a stratified random sample in this situation.
Question 1 The following table shows the number of shirts by sizes that are manufactured in a factory on a particular week: Extra small Small Medium Large Extra Large 390 470 520 680 440 a) It was discovered that the sizing of some shirts was labelled incorrectly. (i) Give two reasons why it would be necessary to examine a sample of the shirts produced rather than examine the entire weekly production. (ii) State two differences between a cluster sample and a stratified random sample in this situation. (iii) Using the stratified random sampling technique, calculate the number of medium shirts that will be selected if we require a sample of 375 shirts. (iv)State one advantage of using stratified random method for collecting this sample. b) Determine the level of measurement that describes the following (i) The size of the shirt that a customer purchase (ii) The total amount paid by the customer (iii) The address of the factory that manufactures the shirts c) A machine packages shirt in bags with a mean weight of 3 kg. A random sample of 20 bags has a mean weight of 3.05 kg with a standard deviation of 0.05kg, From the data given, state the value of a (i) parameter (ii) statistic
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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