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Understanding the central tendency of a dataset is crucial in descriptive statistics. The mean, often referred to as the average, is calculated by summing all the numerical values in a dataset and dividing the sum by the count of the values.

For the given exercise, the mean passive knee extension is calculated as follows:
Mean = \( \frac{(45 + 46 + 49 + 52 + 52 + 56 + 59 + 63 + 64 + 70)}{10} \) = 55.6 degrees.

The mean is sensitive to outliers, which can skew the average. In the absence of significant outliers, as in the exercise, the mean gives a balanced center point of the data.

The median, on the other hand, is the middle value of a dataset when ordered from the least to the greatest, or the average of the two middle values in the case of an even number of observations. The median divides the dataset into two equal halves. For the dataset in the exercise, the median is the average of the 5th and 6th values after sorting the data in ascending order, resulting in a median of 54 degrees.

The median is less affected by outliers or a skewed distribution, making it a robust measure of central tendency when such conditions are present.

The standard deviation is a measure of variability or dispersion in a dataset. It indicates how much individual data points deviate from the mean. To calculate the standard deviation, we first compute the variance, which is the average of the squared differences from the mean. The standard deviation is then the square root of the variance.

For the exercise's dataset, each data point's deviation from the mean is squared, these squared deviations are averaged, and the square root of this average is taken, yielding a standard deviation of 7.86 degrees. This calculation is expressed as:
Standard Deviation = \( \sqrt{\frac{(45-55.6)^2 + (46-55.6)^2 + \cdots + (70-55.6)^2}{10}} \) = 7.86 degrees.

A larger standard deviation indicates greater variability among the data points. When the data points closely cluster around the mean, the standard deviation is smaller. In the context of the exercise, the standard deviation suggests moderate variability in passive knee extension among study participants.

The interquartile range (IQR) is another statistical measure that describes the spread of the middle 50% of a dataset. It is the difference between the third quartile (Q3) and the first quartile (Q1) of the dataset. Quartiles divide the sorted dataset into four equal parts. The IQR is preferred over range because it is not affected by extreme values, known as outliers.

In our exercise, the data is first arranged in ascending order to find the quartiles. The first quartile (Q1) is the median of the lower half, while the third quartile (Q3) is the median of the upper half of the dataset. The IQR is calculated as:
Interquartile Range = Q3 - Q1 = 63 degrees (Q3) - 49 degrees (Q1) = 14 degrees.

The IQR provides a clearer picture of the dataset's central tendency and variability, especially when the mean and standard deviation are less reliable due to skewed data or outliers. In the absence of such issues, the IQR still complements these measures by offering insights into the dataset's range where most data points lie.