An example to calculate mean and standard deviation for a frequency distribution table

mean_stdvariation.py

import numpy as np
import matplotlib.pyplot as plt

# directly listing all the midpoints of the interval using np.linspace
midpoints = np.linspace(5, 95, 10)

# frequency of each interval
freq = np.array([0, 5, 315, 1606, 3105, 2935, 1500, 324, 21, 0])

# elementwise product to get midpoint*frequency
midpt_freq = midpoints*freq

# mean of the frequency distribution
mean = np.sum(midpt_freq)/np.sum(freq)

# variance of the frequency distribution
var = np.sum(freq*(midpoints-mean)**2)/np.sum(freq)

# std deviation is the square root of variance
std = np.sqrt(var)

print("Mean", mean, "Standard deviation", std)