The percentile rank of a score is the percentage of scores in the distribution that are equal to or lower than it.

Percentiles are the values that divide a distribution of scores into one hundred equal parts.
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The #P^{th}# percentile of distribution is the value such that #P# percent of scores are equal to or below it.

Quartiles are the values that divide a distribution of scores into four equal parts.
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The first #(Q_1)#, second #(Q_2)#, and third #(Q_3)# quartiles are equal to the #25^{th}#, #50^{th}#, and #75^{th}# percentile, respectively.

The mode of a distribution is the most frequently observed value.

The median is the midpoint of a distribution. It is the score that divides a distribution into two equal halves.
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The median is equivalent to the #50^{th}# percentile, #P_{50}#, meaning exactly #50\%# of the scores in a distribution are equal to or less than the median (see 'Percentiles').

For a sample of #n# observed values of variable #X#, the sample mean equals:
\[\bar{X}=\cfrac{\sum{X}}{n}\]

The range of a distribution is the difference between the minimum and maximum score:
\[\text{Range}=X_{max}-X_{min}\]

The interquartile range (IQR) of a distribution is the difference between the third and first quartile of a distribution (see 'Quartiles'):
\[\text{IQR}=Q_{3}-Q_{1}\]

The variance of a distribution is the average of the squared deviation scores.
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To calculate the sample variance, make use of the following formula:
\[s^2 = \cfrac{\sum{(X-\bar{X})^2}}{n-1}\]

The standard deviation of a distribution is the positive square root of the variance.
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To calculate the sample standard deviation, make use of the following formula:
\[s = \sqrt{\cfrac{\sum{(X-\bar{X})^2}}{n-1}}\phantom{000}\text{or}\phantom{000}\sqrt{\cfrac{\sum{X^2}-\cfrac{(\sum{X})^2}{n}}{n-1}}\]

A #\boldsymbol{Z}#-score measures a score's distance from the mean in terms of standard deviation units (see 'Standard deviation').
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To turn a sample score #X# into a #Z#-score, make use of the following formula:
\[Z = \cfrac{X - \bar{X}}{s}\]

The covariance measures the direction of the linear relationship between two quantitative variables.
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To calculate the sample covariance between two variables #X# and #Y#, make use of the following formula:
\[s_{\small{X,Y}}=\cfrac{\sum{\bigg((X-\bar{X})(Y-\bar{Y})\bigg)}}{n-1}\]

The Pearson Correlation Coefficient is the standardized form of the covariance (see 'Covariance').
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It is used to measure the direction and strength of the linear relationship between two quantitative variables.
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To calculate the sample Pearson Correlation Coefficient between two variables #X# and #Y#, make use of the following formula:
\[r_{\small{X,Y}}=\cfrac{s_{\small{X,Y}}}{s_{\small{X}} s_{\small{Y}}}=\cfrac{1}{n-1}\sum{\Bigg(\bigg(\cfrac{X - \bar{X}}{s_{\small{X}}} \bigg)\bigg(\cfrac{Y - \bar{Y}}{s_{\small{Y}}} \bigg)\Bigg)}\]