Standard Deviation

Expected Values

The expected value of a discrete random variable, $X$, is more or less another way of referring to the mean ($\mu$). We can also refer to this as the mathematical expectation (or just the expectation) of $X$.

Variance $\sigma^2$

This is the average magnitude of fluctuations of $X$ from its expected value, $\mu$. You can also think of it as the expectation of a random variable's squared deviation from its mean. Given a data set, $X$, of size :

$\sigma^2 = \frac{\sum_{i=1}^n (x_i - \mu)^2}{n}$

where $x_i$ is the $i^{th}$ element of the data set and $\mu$ is the mean of all the elements.

Standard Deviation $\sigma$

The standard deviation quantifies the amount of variation in a set of data values. Given a data set, $X$, of size :

$\sigma = \sqrt{\frac{\sum_{i=1}^n (x_i - \mu)^2}{n}}$

where $x_i$ is the $i^{th}$ element of the data set and $\mu$ is the mean of all the elements.

import math

num = int(input())
values = list(map(int, input().split()))

mean = sum(values)/num

result = 0
for i in values:
    result += (i - mean)**2

print('%.1f' % math.sqrt(result/num))

Interquartile Range

num = 5
elements = [10, 40, 30, 50, 20]
freq = [1, 2, 3, 4, 5]

values = []
for k, v in enumerate(elements):
    values.extend([v] * freq[k])
values.sort()

lower = values[:len(values)//2]
upper = values[len(values)//2:]

num = len(values)-1
if num % 2 == 0:
    lower = values[:len(values)//2]
    upper = values[len(values)//2:]
else:
    lower = values[:len(values)//2]
    upper = values[len(values)//2:]
    lower.append(upper[0])

if len(lower) % 2 == 0:
    v1 = lower[int(len(lower)/2)-1]
    v2 = lower[int(len(lower)/2)]
    q1 = (v1+v2)/2
    v1 = upper[int(len(upper)/2)-1]
    v2 = upper[int(len(upper)/2)]
    q3 = (v1+v2)/2
else:
    q1 = lower[int(len(lower)/2)]
    q3 = upper[int(len(upper)/2)]

print(float(q3 - q1))