Lesson 15 Statistics

Question 1

Import the packages for maths, stats and scipy

Answer 1

import math
import statistics
import numpy as np
import scipy.stats
import pandas as pd

Question 2

Create a list inserting a nan between 2.5 and 4

x = [8.0, 1, 2.5, 4, 28.0]

Answer 2

x_with_nan = [8.0, 1, 2.5, math.nan, 4, 28.0]

Question 3

What are the three different ways of getting a nan value?

Answer 3

• float(‘nan’)
• math.nan
• np.nan

Question 4

Create np.ndarray and pd.Series objects that correspond to x and x_with_nan from the following lists:

x = [8.0, 1, 2.5, 4, 28.0]

x_with_nan = [8.0, 1, 2.5, math.nan, 4, 28.0]

Answer 4

y, y_with_nan = np.array(x), np.array(x_with_nan)
z, z_with_nan = pd.Series(x), pd.Series(x_with_nan)

Question 5

Find the mean using in in built python function.

Answer 5

mean_ = statistics.mean(x)
mean_

Question 6

What is another function to calculate the mean?

Answer 6

mean_ = statistics.fmean(x)
mean_

Question 7

What value will the mean return if there are nan values present?

Answer 7

nan

Question 8

How do you calculate the mean with numpy

Answer 8

mean_ = np.mean(y)
mean_

Question 9

Write the code to calculate the mean but ignore any Nan values.

Answer 9

np.nanmean(y_with_nan)

Question 10

x = [8.0, 1, 2.5, 4, 28.0]
w = [0.1, 0.2, 0.3, 0.25, 0.15]

y, z, w = np.array(x), pd.Series(x), np.array(w)
wmean = np.average(y, weights=w)
print(wmean)

Calculate the weighted mean of NumPy array or Pandas series

wmean = np.average(z, weights=w)

Answer 10

wmean = np.average(z, weights=w)

Question 11

Calculate the harmonic mean using statistics library

Answer 11

hmean = statistics.harmonic_mean(x)

Question 12

What happens if you input the following for a harmonic mean:

nan value
0
negative number

Answer 12

nan
0
error

Question 13

Calculate the geometric mean

Answer 13

gmean = statistics.geometric_mean(x)

Question 14

What is the main difference btween the behaviour of the mean and median?

Answer 14

The main difference between the behavior of the mean and median is related to dataset outliers or extremes. The mean is heavily affected by outliers, but the median only depends on outliers either slightly or not at all.

Question 15

x is [1, 2.5, 4, 8.0, 28.0]

Find the median of the list x

Answer 15

median_ = statistics.median(x)

Question 16

x is [1, 2.5, 4, 8.0, 28.0]. Slice the list so you remove the 28.0 and find the median.

Answer 16

median_ = statistics.median(x[:-1])

Question 17

If the number of elements is even there are two middle values: find the lower median value from this list:

x is [1, 2.5, 4, 8.0, 28.0]

Answer 17

statistics.median_low(x[:-1])

Question 18

If the number of elements is even there are two middle values: find the higher median value from this list:

x is [1, 2.5, 4, 8.0, 28.0]

Answer 18

statistics.median_high(x[:-1])

Question 19

Calculate the mode returning a single value.

Answer 19

mode_ = statistics.mode(u)

Question 20

Calculate the mode returning all modes

Answer 20

mode_ = statistics.multimode(u)

Question 21

Calculate the mode using the following series (finish the code):

u, v, w = pd.Series(u), pd.Series(v), pd.Series(

Answer 21

u, v, w = pd.Series(u), pd.Series(v), pd.Series([2, 2, math.nan])

Question 22

Calculate the variance

Answer 22

var_ = statistics.variance(x)

Question 23

Calculate the variance using NumPy

Answer 23

var_ = np.var(y, ddof=1)
OR
var_ = y.var(ddof=1)

Question 24

Calculate the variance to include nans

Answer 24

np.nanvar(y_with_nan, ddof=1)

Question 25

Calculate variance with pandas (it will automatically include nans).

Answer 25

z_with_nan.var(ddof=1)

Question 26

Calculate the standard deviation

Answer 26

std_ = statistics.stdev(x)

Question 27

Use numpy to calculate standard deviation

Answer 27

np.std(y, ddof=1)
OR

y.std(ddof=1)

Question 28

Use this list to show the sample 25th and 75th percentiles.

x = [-5.0, -1.1, 0.1, 2.0, 8.0, 12.8, 21.0, 25.8, 41.0]

Answer 28

x = [-5.0, -1.1, 0.1, 2.0, 8.0, 12.8, 21.0, 25.8, 41.0]
statistics.quantiles(x, n=4, method=’inclusive’)

Question 29

x = [-5.0, -1.1, 0.1, 2.0, 8.0, 12.8, 21.0, 25.8, 41.0]

y = np.array(x)

In a given array x, find the 5th percentile
FInd the 95th percentile

Answer 29

find 5th percentile
np.percentile(y, 5)

find 95th percentile
np.percentile(y, 95)

Question 30

Find the percentil in an array with nan values

Answer 30

np.nanpercentile(y_with_nan, [25, 50, 75])

Question 31

Make a cov matrix to show the correlation coefficients from the following arrays:

np.array([14.2, 16.4,15.2, 22.6, 17.2])
np.array([215,325, 332, 445, 408])

Answer 31

cov_matrix = np.corrcoef(np.array([14.2, 16.4,15.2, 22.6, 17.2]), np.array([215,325, 332, 445, 408]))