Calculate the Mean
Average Calculation
To find the mean, sum all the values and divide by the number of values. The sum is \(1.0 + 1.2 + 1.5 + 2.0 + 2.2 + 2.5 + 2.8 + 3.0 + 3.2 + 3.5 + 3.7 + 4.0 + 4.3 + 4.5 + 5.0 + 5.5 + 5.8 + 6.0 + 6.5 + 7.0 = 75.2\). There are 20 values, so the mean is \(75.2 / 20 = 3.76\).
\(\boxed{\text{Mean} = 3.76}\)
Calculate the Median
Middle Value Identification
The median is the middle value of the sorted data. With 20 values, the median is the average of the 10th and 11th values. The 10th value is 3.5 and the 11th value is 3.7, so the median is \((3.5 + 3.7) / 2 = 3.6\).
\(\boxed{\text{Median} = 3.6}\)
Calculate the Mode
Most Frequent Value Identification
The mode is the value that appears most frequently. Each value appears only once, so there is no mode.
\(\boxed{\text{Mode} = \text{None}}\)
Calculate the Range
Difference Between Maximum and Minimum
The range is the difference between the maximum and minimum values. The maximum value is 7.0 and the minimum value is 1.0, so the range is \(7.0 - 1.0 = 6.0\).
\(\boxed{\text{Range} = 6.0}\)
Calculate the Standard Deviation
Standard Deviation Calculation
First, find the variance by calculating the average of the squared differences from the mean. The squared differences are \((1.0 - 3.76)^2, (1.2 - 3.76)^2, \ldots, (7.0 - 3.76)^2\). The sum of these squared differences is 61.25. Divide by the number of values to get the variance: \(61.25 / 20 = 3.0625\). The standard deviation is the square root of the variance: \(\sqrt{3.0625} \approx 1.75\).
\(\boxed{\text{Standard Deviation} = 1.75}\)
Calculate the Coefficient of Variation
Coefficient of Variation Calculation
The coefficient of variation is the ratio of the standard deviation to the mean, expressed as a percentage. It is \((1.75 / 3.76) \times 100\% \approx 46.42\%\).
\(\boxed{\text{Coefficient of Variation} = 46.42\%}\)
\(\boxed{\text{Mean} = 3.76}\)
\(\boxed{\text{Median} = 3.6}\)
\(\boxed{\text{Mode} = \text{None}}\)
\(\boxed{\text{Range} = 6.0}\)
\(\boxed{\text{Standard Deviation} = 1.75}\)
\(\boxed{\text{Coefficient of Variation} = 46.42\%}\)
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