Let's go through each of the calculations step by step.

Given data:
$8, 9, 11, 12, 7, 16, 23, 13, 18, 14, 5, 8$
Standard deviation $S = 5$.

1. Mean

The mean $\bar{x}$ is calculated as the sum of all values divided by the number of values: $\bar{x} = \frac{8 + 9 + 11 + 12 + 7 + 16 + 23 + 13 + 18 + 14 + 5 + 8}{12}$

$\bar{x} = \frac{144}{12} = 12$

Mean = 12

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2. Median

To find the median, we first need to arrange the numbers in ascending order: $5, 7, 8, 8, 9, 11, 12, 13, 14, 16, 18, 23$ Since there are 12 values (even number), the median is the average of the 6th and 7th values: $\text{Median} = \frac{11 + 12}{2} = \frac{23}{2} = 11.5$

Median = 11.5

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3. Mode

The mode is the value that appears most frequently in the data. In this case, the number 8 appears twice.

Mode = 8

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4. Range

The range is the difference between the maximum and minimum values: $\text{Range} = 23 - 5 = 18$

Range = 18

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5. Coefficient of Variation (C.V.)

The coefficient of variation is calculated as: $\text{C.V.} = \left( \frac{\text{Standard Deviation}}{\text{Mean}} \right) \times 100$ Given that the standard deviation $S = 5$ and the mean $\bar{x} = 12$: $\text{C.V.} = \left( \frac{5}{12} \right) \times 100 = 41.67\%$

Coefficient of Variation (C.V.) = 41.67%

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6. Z18 (Z-score for the value 18)

The Z-score for a given value $x$ is calculated as: $Z_x = \frac{x - \bar{x}}{S}$ For $x = 18$, $\bar{x} = 12$, and $S = 5$: $Z_{18} = \frac{18 - 12}{5} = \frac{6}{5} = 1.2$

Z18 = 1.2

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Would you like further details on any of these calculations?

Related Questions:

1. How do you calculate variance from the given data?
2. What is the significance of the Z-score in statistics?
3. How do you determine if data is normally distributed using the mean and standard deviation?
4. What is the difference between population standard deviation and sample standard deviation?
5. How does the coefficient of variation help in comparing data sets?

Tip: Always verify if the given standard deviation is sample or population-based before performing further calculations.