Python for Data Science: Laboratory Programs in Python
Statistical description of data without libraries
Laboratory Programs in Python
Python for Data Science: Laboratory Programs in Python: Descriptive Analytics: Statistical description of data without libraries
Normal distribution formula
Mathematically the Probability Density Function (PDF) of normal distribution is
where:
x = Value in the dataset
μ = Mean (average)
σ = Standard deviation (Spread of data)
e = Euler's number (≈ 2.718)
Ex 1.
A random variable X follows a normal distribution with mean of 10 and a standard deviation of 2. Find the value of the Probability Density Function (PDF) at x = 12.
Solution: The formula for finding PDF is
Given that:
(μ = 10, σ = 2, x = 12):
Simplify the exponent:
[(12‒10)2 ] / 2.22 = 4/8 = 0.5
The formula now becomes
f(12) = [ 1 / 2√2π ] e ‒0.5
√2π ≈ 2.5066,
e‒0.5 ≈ 0.6065.
f(12) = [1 / 2×2.5066 ] . 0.6065
= 0.6065 / 5.0132 ≈ 0.1210
Hence, the value of the PDF at x = 12 is approximately 0.1210
Formula:
z = (X ‒μ) / σ
where
X = Individual value
μ = Mean
σ = Standard deviation
Ex 2.
Consider Mean = 70, Standard deviation = 10, and student's score is 85. Calculate Z score and interpret your answer.
Solution :
The z score can be calculated as
z = (X ‒μ) / σ = (85‒70) / 10
z = 1.5
Interpretation: The student scored is standard deviation above mean. That means this student has scored better than most of the students.
Ex 3.
Consider mean height = 165 cm, σ = 5 cm, X = 155 cm. Calculate z score and interpreter your result.
Solution :
z = (155‒165) / 5 = ‒2
Interpretation: The height is 2 standard deviations below mean. So the height of student is short as compared to average.
Python for Data Science: Laboratory Programs in Python : Tag: Computer Programming, Python, Data Science : Laboratory Programs in Python - Statistical description of data without libraries
Python for Data Science: Laboratory Programs in Python
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