Mean: also known as the average is a measure of central tendency in a dataset. It is calculated by summing up all the values in the dataset and dividing the sum by the total number of values.
Standard deviation: The standard deviation is a measure of the dispersion of data around the mean in a dataset.t quantifies the average amount by which each data point in the dataset varies from the mean. A higher standard deviation indicates greater variability or dispersion of the data points, while a lower standard deviation suggests that the data points are closer to the mean. The standard deviation is typically represented by the symbol σ (sigma).
Z-Score: The z-score (also known as the standard score) is a statistical measurement that indicates how many standard deviations an individual data point is from the mean of a distribution. It allows you to compare and understand the relative position of a particular data point within a dataset.
The formula to calculate it is: Z = (x - μ) / σ where:
Z = Z-score
x = data point
μ = mean
σ = standard deviation
To calculate the z-score for Luis's exam grade, we can use the formula:
z = (x - μ) / σ
Where:
x = Luis's exam grade (84)
μ = Mean (81)
σ = Standard deviation (2.5)
Substituting the given values into the formula, we have:
z = (84 - 81) / 2.5
z = 3 / 2.5
z = 1.20
Rounding to two decimal places, the z-score for Luis's exam grade is 1.20.