Page 266 - Artificial Intellegence_v2.0_Class_11
P. 266
Z-scores
A statistical measurement known as the Z-score indicates how closely a value relates to the mean of a group of values.
The Z-score is calculated using standard deviations from the mean. When a data point's Z-score is 0, it means that it has
the same score as the mean. One standard deviation from the mean would be indicated by a Z-score of 1.0. Z-scores can
be positive or negative; a positive value means the score is above the mean, while a negative value means it is below the
mean. Z-score can be calculated using the following formula:
z = ( x - μ ) / σ
where:
• z = Z-score
• x = the value being evaluated
• μ = the mean
• σ = the standard deviation
Example:
x = 59
μ = 52
σ = 4
Applying the formula, z = (59 - 52 ) / 4, z = 1.75
So, your selected value has a z-score that indicates it is 1.75 standard deviations from the mean.
At a Glance
• Statistical methods are required to understand the data used to train a machine learning model and to
interpret the results of testing different machine learning models.
• Structured data is formatted, and has a predefined data type and arrangement.
• A variable is a characteristic that is measured and can have multiple values. In other words, something that
varies from case to case.
• The level of measurement refers to the relationship between the values given to the attributes of a variable.
• In nominal measurement, the numerical values represent a unique “name” of the attribute.
• In ordinal measurement, attributes can be ordered. The distances or intervals between attributes are irrelevant
here.
• While measuring intervals, the distance between attributes is important.
• Ratio measurements are based on proportion and can have an absolute zero value.
• The tabular format to present cases and variables used in statistical study is known as a data matrix.
• The frequency of a particular data value is the number of occurrences of that data value in a dataset.
• The shape of data distribution in a graph is described by its number of peaks and their symmetry, their
tendency to skew, or their uniformity.
• A graph can be unimodal, bimodal or multimodal.
• Distribution is symmetric if its left half forms a mirror image of its right half.
• A distribution that is not symmetric has values that tend to be more spread out on one side of the graph
than on the other.
• A distribution that is not symmetric can be left-skewed or right-skewed.
• In Symmetric distribution, the median, mean, and mode are the same.
• The mean is the average or the most common value in a group of numbers.
• The median is the middle value in a given list of numbers arranged in ascending or descending order.
• The mode is the value that appears most often in a given list of numbers.
264 Touchpad Artificial Intelligence (Ver. 2.0)-XI

