An auditor detects that a firm is regularly overstating the amounts of inventories because of delays in recording withdrawals. He takes a random sample of 20 inventories and finds that they are overstated by the following amounts (in pounds sterling) 10 12 9 28 6 20 26 24 12 22 5 14 11 23 9 21 29 13 16 24
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
An auditor detects that a firm is regularly overstating the amounts of inventories because of delays in recording withdrawals. He takes a random sample of 20 inventories and finds that they are overstated by the following amounts (in pounds sterling)
10 12 9 28 6 20 26 24 12 22 5 14 11 23 9 21 29 13 16 24
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(d) Calculate the sample mean and the sample
median , and compare these two values. Which of these two values is more ‘informative’? -
(e) Calculate the
range and theinterquartile range of the data. -
(f) Calculate the sample variance, the sample standard deviation and the coefficient of variation.
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