# statistics¶

Source code: statistics.seq

exception statistics.StatisticsError

Properties:

message

Magic methods:

__init__()
__init__(message: str)
statistics.median[T](data: list[T])

Return the median (middle value) of numeric data.

When the number of data points is odd, return the middle data point. When the number of data points is even, the median is interpolated by taking the average of the two middle values

statistics.median_low[T](data: list[T])

Return the low median of numeric data.

When the number of data points is odd, the middle value is returned. When it is even, the smaller of the two middle values is returned.

statistics.median_high[T](data: list[T])

Return the high median of data.

When the number of data points is odd, the middle value is returned. When it is even, the larger of the two middle values is returned.

statistics.median_grouped[T, S](data: list[T], interval: S = 1)

Return the 50th percentile (median) of grouped continuous data.

statistics.mode[T](data: list[T])

Return the most common data point from discrete or nominal data.

statistics.multimode[T](data: list[T])

Return a list of the most frequently occurring values.

Will return more than one result if there are multiple modes or an empty list if data is empty.

statistics.quantiles[T](data: list[T], n: int = 4, method: str = 'exclusive')

Divide data into n continuous intervals with equal probability.

Returns a list of (n - 1) cut points separating the intervals.

Set n to 4 for quartiles (the default). Set n to 10 for deciles. Set n to 100 for percentiles which gives the 99 cuts points that separate data in to 100 equal sized groups.

The data can be any iterable containing sample. The cut points are linearly interpolated between data points.

If method is set to inclusive, data is treated as population data. The minimum value is treated as the 0th percentile and the maximum value is treated as the 100th percentile.

statistics.as_integer_ratio(x: float)

as_integer_ratio()

Express a float in the form n / d.

Returns a pair (n, d) of integers.

statistics.mean(data: list[float])

Return the sample arithmetic mean of data.

TODO/CAVEATS
• Assumes input is floats

• Does not address NAN or INF

statistics.geometric_mean(data: list[float])

Convert data to floats and compute the geometric mean.

Raises a StatisticsError if the input dataset is empty,

TODO/CAVEATS:
• Assumes input is a list of floats

• Uses mean instead of fmean for now

• Does not handle data that contains a zero, or if it contains a negative value.

statistics.harmonic_mean(data: list[float])

Return the harmonic mean of data.

The harmonic mean, sometimes called the subcontrary mean, is the reciprocal of the arithmetic mean of the reciprocals of the data, and is often appropriate when averaging quantities which are rates or ratios.

statistics.pvariance(data: list[float], mu: optional[float] = None)

Return the population variance of data.

Should contain atleast one value. The optional argument mu, if given, should be the mean of the data. If it is missing or None, the mean is automatically calculated.

TODO/CAVEATS:
• Assumes input is a list of floats

statistics.pstdev(data: list[float], mu: optional[float] = None)

Return the square root of the population variance.

statistics.variance(data: list[float], xbar: optional[float] = None)

Return the sample variance of data.

Shoulw contain atleast two values. The optional argument xbar, if given, should be the mean of the data. If it is missing or None, the mean is automatically calculated.

statistics.stdev(data, xbar: optional[float] = None)

Return the square root of the sample variance.

class statistics.NormalDist

Normal distribution of a random variable

Properties:

mean

Arithmetic mean of the normal distribution.

median

Return the median of the normal distribution

mode

Return the mode of the normal distribution

The mode is the value x where which the probability density function (pdf) takes its maximum value.

stdev

Standard deviation of the normal distribution.

variance

Square of the standard deviation.

Magic methods:

__eq__(other: NormalDist)
__init__(mu: float, sigma: float)
__init__(mu: int, sigma: int)
__init__(mu: float, sigma: int)
__init__(mu: int, sigma: float)
__init__(mu: float)
__init__(mu: int)
__init__()
__add__(x1: NormalDist, x2: NormalDist)

Add a constant or another NormalDist instance. If other is a constant, translate mu by the constant, leaving sigma unchanged. If other is a NormalDist, add both the means and the variances. Mathematically, this works only if the two distributions are independent or if they are jointly normally distributed.

__add__(x1: NormalDist, x2: float)

Add a constant or another NormalDist instance. If other is a constant, translate mu by the constant, leaving sigma unchanged. If other is a NormalDist, add both the means and the variances. Mathematically, this works only if the two distributions are independent or if they are jointly normally distributed.

__sub__(x1: NormalDist, x2: NormalDist)

Subtract a constant or another NormalDist instance. If other is a constant, translate by the constant mu, leaving sigma unchanged. If other is a NormalDist, subtract the means and add the variances. Mathematically, this works only if the two distributions are independent or if they are jointly normally distributed.

__sub__(x1: NormalDist, x2: float)

Subtract a constant or another NormalDist instance. If other is a constant, translate by the constant mu, leaving sigma unchanged. If other is a NormalDist, subtract the means and add the variances. Mathematically, this works only if the two distributions are independent or if they are jointly normally distributed.

__mul__(x1: NormalDist, x2: float)

Multiply both mu and sigma by a constant. Used for rescaling, perhaps to change measurement units. Sigma is scaled with the absolute value of the constant.

__truediv__(x1: NormalDist, x2: float)

Divide both mu and sigma by a constant. Used for rescaling, perhaps to change measurement units. Sigma is scaled with the absolute value of the constant.

__pos__(x1: NormalDist)
__neg__(x1: NormalDist)
__radd__(x1: NormalDist, x2: float)
__rsub__(x1: NormalDist, x2: NormalDist)
__rmul__(x1: NormalDist, x2: float)
__eq__(x1: NormalDist, x2: NormalDist)
__hash__()
__str__()

Methods:

pdf(x)

Probability density function. P(x <= X < x+dx) / dx

cdf(x)

Cumulative distribution function. P(X <= x)

inv_cdf(p: float)

Inverse cumulative distribution function. x : P(X <= x) = p

Finds the value of the random variable such that the probability of the variable being less than or equal to that value equals the given probability.

quantiles(n: int = 4)

Divide into n continuous intervals with equal probability.

Returns a list of (n - 1) cut points separating the intervals.

Set n to 4 for quartiles (the default). Set n to 10 for deciles. Set n to 100 for percentiles which gives the 99 cuts points that separate the normal distribution in to 100 equal sized groups.

overlap(other: NormalDist)

Compute the overlapping coefficient (OVL) between two normal distributions.

Measures the agreement between two normal probability distributions. Returns a value between 0.0 and 1.0 giving the overlapping area in the two underlying probability density functions.

samples[T](n: int)

Generate n samples for a given mean and standard deviation.

from_samples(data: list[float])

Make a normal distribution instance from sample data. TODO/CAVEATS:

• Assumes input is a list of floats

• Uses mean instead of fmean for now