Computer Science
Topic 1. Descriptive
Statistics
1)The Mean:
Overview of Mean
● The mean is a measure of central tendency in a population or
sample.
● It is denoted by the Greek letter mu and is calculated by summing
all the observations and dividing by their total number.
● For samples, the lowercase n is used instead of an uppercase N.
Mean in Action
● To find the mean of a sample, add all the observations and divide
by the total number of observations.
● For example, the mean of the sample 10, 28, 33 and 54 is 30.6.
● As a convention, the mean is provided to one more decimal place
than the original data set was given in.
Advanced Mean
, ● To calculate a weighted mean, multiply each observation by its
frequency and divide by the total number of observations.
● This can also be expressed as summing the products of the
observations and their frequencies, divided by the sum of the
frequencies.
● The mean can also be calculated for categorical variables.
● Finally, a challenge question can be posed to test understanding of
the mean.
Formula for calculating mean
● A formula for calculating the mean looks ugly but should be quite
intuitive.
● It involves multiplying all the values of X by their frequencies and
summing them up, then dividing by the sum of all frequencies.
Calculating mean of categorical data set
● It is possible to find the mean of a categorical data set by defining
all the females as ones and males as zeros, making it a numerical
data set.
● To calculate the mean, add up all of those values and divide by the
total number of values.
● The mean of a binary variable gives you the proportion of the
category that we defined as 1.
Georgia's challenge
● Georgia's challenge is to calculate her weighted average mark that
she's got from her statistics degree thus far.
● She has done 4 subjects and has marks and credit points for each
of them.
● To calculate her weighted average mark, she must incorporate the
credit point information.
, 2) Arithmetic Mean | Geometric
Mean | Harmonic Mean:
Introduction the Mean
● The earliest reference to the word "mean" comes from the 1300s
French, and was initially used to describe the middle point
between two musical notes.
● The basics of calculating the mean are straightforward: using the
Greek letter x-bar to represent the sample mean, and the Greek
letter mu to represent the population mean.
Calculating the Mean
● To calculate the sample mean, the sum of the observations
(indicated by the Greek letter sigma) must be divided by the
number of observations (indicated by the letter n).
● An example of calculating the mean is given, showing the average
height of five professional basketball players as 2.03 meters.
● This mean is an estimate of the true, unknowable population
mean.
Other Types of Means
● Other types of means include the geometric mean which involves
finding the product of the observations and taking the nth root of
the product.
● The harmonic mean involves inverting the observations, finding the
average of the inverted observations, and then inverting the
average.
● The arithmetic mean is the one used most often, and is what has
been referred to as "mean" up to this point in the video.
Topic 1. Descriptive
Statistics
1)The Mean:
Overview of Mean
● The mean is a measure of central tendency in a population or
sample.
● It is denoted by the Greek letter mu and is calculated by summing
all the observations and dividing by their total number.
● For samples, the lowercase n is used instead of an uppercase N.
Mean in Action
● To find the mean of a sample, add all the observations and divide
by the total number of observations.
● For example, the mean of the sample 10, 28, 33 and 54 is 30.6.
● As a convention, the mean is provided to one more decimal place
than the original data set was given in.
Advanced Mean
, ● To calculate a weighted mean, multiply each observation by its
frequency and divide by the total number of observations.
● This can also be expressed as summing the products of the
observations and their frequencies, divided by the sum of the
frequencies.
● The mean can also be calculated for categorical variables.
● Finally, a challenge question can be posed to test understanding of
the mean.
Formula for calculating mean
● A formula for calculating the mean looks ugly but should be quite
intuitive.
● It involves multiplying all the values of X by their frequencies and
summing them up, then dividing by the sum of all frequencies.
Calculating mean of categorical data set
● It is possible to find the mean of a categorical data set by defining
all the females as ones and males as zeros, making it a numerical
data set.
● To calculate the mean, add up all of those values and divide by the
total number of values.
● The mean of a binary variable gives you the proportion of the
category that we defined as 1.
Georgia's challenge
● Georgia's challenge is to calculate her weighted average mark that
she's got from her statistics degree thus far.
● She has done 4 subjects and has marks and credit points for each
of them.
● To calculate her weighted average mark, she must incorporate the
credit point information.
, 2) Arithmetic Mean | Geometric
Mean | Harmonic Mean:
Introduction the Mean
● The earliest reference to the word "mean" comes from the 1300s
French, and was initially used to describe the middle point
between two musical notes.
● The basics of calculating the mean are straightforward: using the
Greek letter x-bar to represent the sample mean, and the Greek
letter mu to represent the population mean.
Calculating the Mean
● To calculate the sample mean, the sum of the observations
(indicated by the Greek letter sigma) must be divided by the
number of observations (indicated by the letter n).
● An example of calculating the mean is given, showing the average
height of five professional basketball players as 2.03 meters.
● This mean is an estimate of the true, unknowable population
mean.
Other Types of Means
● Other types of means include the geometric mean which involves
finding the product of the observations and taking the nth root of
the product.
● The harmonic mean involves inverting the observations, finding the
average of the inverted observations, and then inverting the
average.
● The arithmetic mean is the one used most often, and is what has
been referred to as "mean" up to this point in the video.
