Write a program in a file named histogram.py that displays the histogram depicted in Figure $11-7.$

$"""$

File: stats.py

Defines functions to compute the mean, median, std$,$ and mode

of a list of numbers.

$"""$

import math

import random

def mean$($lyst$)$:

$"""$Returns the mean of a list of numbers."""

return sum$($lyst$)/$ len$($lyst$)$

def frequencies$($lyst$)$:

$"""$Returns a dictionary keyed by the unique

numbers and their frequencies in lyst$."""$

# Obtain the set of unique numbers and their

# frequencies, saving these associations in

# a dictionary

theDictionary $=\{\}$

for number in lyst:

freq $=$ theDictionary.get$($number$,0)$

theDictionary$[$number$]=$ freq $+1$

return theDictionary

def mode$($lyst$)$:

$"""$Returns the mode of a list of numbers."""

theDictionary $=$ frequencies$($lyst$)$

theMaximum $=$ max$($theDictionary$.$values$())$

for key in theDictionary:

if theDictionary$[$key$]==$ theMaximum:

result $=$ key

break

return result

def modes$($lyst$)$:

$"""$Returns the modes of a list of numbers."""

# Obtain the set of unique numbers and their

# frequencies, saving these associations in

# a dictionary

theDictionary $=$ frequencies$($lyst$)$

theMaximum $=$ max$($theDictionary$.$values$())$

result $=[]$

for key in theDictionary:

if theDictionary$[$key$]==$ theMaximum:

result.append$($key$)$

return result

def median$($lyst$)$:

$"""$Precondition: lyst is non$-$empty.

Returns the median of numbers in lyst$."""$

if len$($lyst$)==0$:

raise RuntimeError$("$List must be non$-$empty. $")$

copy $=$ list$($lyst$)$

copy.sort$()$

midpoint $=$ len$($lyst$)//2$

if len$($lyst$)\%2==1$:

return copy$[$midpoint$]$

else:

return mean$([$copy$[$midpoint $-1],$ copy$[$midpoint$]])$

def std$($lyst$)$:

$"""$Precondition: lyst is non$-$empty.

Returns the standard deviation of the numbers in lyst$."""$

if len$($lyst$)==0$:

raise RuntimeError$("$List must be non$-$empty. $")$

average $=$ mean$($lyst$)$

differences $=$ map$($lambda x: x $-$ average, lyst$)$

squares $=$ list$($map$($lambda x: x $**2,$ differences$))$

return math.sqrt$($mean$($squares$))$

def getRandomList$($size$,$ lower, upper, unique $=$ False$)$:

$"""$Returns a list of randomly generate numbers

within the given bounds."""

theList $=[]$

for count in range$($size$)$:

number $=$ random.randint$($lower$,$ upper$)$

if unique:

while number in theList:

number $=$ random.randint$($lower$,$ upper$)$

theList.append$($number$)$

return theList

def main$()$:

$"""$Tests the functions."""

lyst $=[3,1,7,1,4,10]$

print$("$List:$",$ lyst$)$

print$("$Mode:$",$ mode$($lyst$))$

print$("$Median:$",$ median$($lyst$))$

print$("$Mean:$",$ mean$($lyst$))$

print$("$Standard deviation:", std$($lyst$))$

print$("$Frequencies:$",$ frequencies$($lyst$))$

lyst$.$sort$()$

print$($lyst$)$

lyst $=[3,1,7,1,4]$

print$("$List:$",$ lyst$)$

print$("$Mode:$",$ mode$($lyst$))$

print$("$Median:$",$ median$($lyst$))$

print$("$Mean:$",$ mean$($lyst$))$

print$("$Standard deviation:", std$($lyst$))$

print$("$Frequencies:$",$ frequencies$($lyst$))$

lyst$.$sort$()$

print$($lyst$)$

lyst $=$ getRandomList$(10,1,10)$

print$($lyst$)$

lyst $=$ getRandomList$(10,1,10,$ unique $=$ True$)$

print$($lyst$)$

# The entry point for program execution

if $\_\_$name$\_\_=="\_\_$main$\_\_"$:

main$()$Figure $1$