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 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 (a) Make a relative frequency table of the data using groups 5−9, 10−14, . . . technically, such groups are known as bins. (b) Draw a frequency histogram of the data. (c) Describe the shape of the distribution of the data, commenting on any interesting features. (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 the interquartile range of the data. (f) Calculate the sample variance, the sample standard deviation and the coefficient of variation
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
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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(a) Make a relative frequency table of the data using groups 5−9, 10−14, . . . technically, such groups are known as bins.
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(b) Draw a frequency histogram of the data.
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(c) Describe the shape of the distribution of the data, commenting on any interesting features.
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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’?
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(e) Calculate the
range and theinterquartile range of the data. -
(f) Calculate the sample variance, the sample standard deviation and the coefficient of variation.
Note: According to the guidelines, only first three subparts have been solved.
Given:
The random sample of 20 inventories are:
10, 12, 9, 28, 6, 20, 26, 24, 12, 22, 5, 14, 11, 23, 9, 21, 29, 13, 16, 24
a)
The class interval is 5-9,10-14....
The relative frequency table is:
| Bins | Frequency | Relative frequency |
| 5-9 | 4 | |
| 10-14 | 6 | |
| 15-19 | 1 | |
| 20-24 | 6 | |
| 25-29 | 3 |
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