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Mean Median Mode | Darwin Ong | YouTubeToText
YouTube Transcript: Mean Median Mode
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Video Summary
Summary
Core Theme
This content introduces fundamental statistical concepts for describing data, focusing on measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation), along with frequency distributions and histograms.
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we are going to discuss this describing data
data
with your numerical measures
so our goal is to calculate the
arithmetic mean
weighted mean median mode and geometric mean
mean
and then we can explain the
characteristic uses the advantages
and disadvantages of each measure of locations
locations
and we can identify the position of the
mean median
and mode for both symmetric and good distributions
distributions
and we can compute and interpret the
range mean division variance and standard
standard
deviation okay first
we're going to discuss the frequency
distribution this is a table that
organizes the data values in
into classes on intervals along with number
number
of of values that fall in each class
so it this will be your frequency summation
sun group frequency distribution
for data sets with few different
values each value is in its own class
for the group of frequency distribution
for data sets with many different values
which are grouped together in
classes so if you adding
30 we have 202 i'm frequenting yeah
so 32 42 we have one 508
43 and 50 54 so we have 620
for 55 to 66 we have 413
67 to 78 is 158
78 to 90 is 32.
difference category we have ungroup
and group and then for example
for the ungroup frequency distribution
one
four and five so we have five
ah so four one
two three
four five six
seven eight and nine adiva
so gonna think it's a five in eight and
so for the frequency histogram a bar
graph that represents the frequency distribution
distribution
so the horizontal scale is the quantitative
quantitative
and measured the data values yes horizontal
horizontal
unlike this vertical iteration measures
that non-frequency of classes
frequent and just a five month frequency
so four
adjectives are nine and so five
okay next so it's a relative
frequency distribution shows shows the
proportion of percent or percentage of
the data
that falls in a particular class for
example we have relative frequency is
equal to
class frequency over the sample size
so relative frequency histogram has the
same shape
and the same horizontal scale as the
corresponding frequency
histogram so the vertical scale
measures the relative frequencies not
frequencies relative frequencies
not the frequencies okay so
has the same shape and horizontal scale
as a and as a histogram but
the the vertical scale is marked with
relative frequencies so get reading
samples so
this will be our relative frequency
30 35 percent three percent and five
percent so it's
a thing a sample started
for the data sets with many different
values for the group frequency distribution
distribution
so group theta into 5 to 20 classes of equal
equal
with you know fdm frequency n
okay for example yeah it's got exam scores
scores
40 to 4959 in london 69 in london
and then 7279 illandin
and so on and so forth for example
so 30-30 is a 40-49
0. there is a 50-59 up but
nine 66-69 seven and thirteen and diamond
so eighty to eighty one nine is we have
ten then nineteen to ninety nine we have three
three diva
for the lower class limits are the
smallest number
that can actually belong to the
different classes
for the upper class limits are the largest
largest
numbers that can actually belong to
different classes
class feed is the difference between two
or later on okay okay
so the class midpoint actually the value
halfway between
lower class limit and then the upper
class boundaries demand class halfway between
between
an upper class limit and the next lower
upper class limit plus the next lower
class limit over to
okay so what are the characteristics of
of the mean so the arithmetic mean is
the most
widely used measure of location it may require
require
requires the interval scale its major
characteristics are all values are used
the sum of deviation from the mean is zero
zero
it is unique and it is
calculated by summing the values
and dividing the number of values actually
so we have two types of means so we have
the population mean and then the sample mean
mean
for the population mean for ungroup data
the population mean
is the sum of all the population values
divided by the total number of population
population
values so we have population mean so
summation of
x over and where x is representing any
particular value
mean nothing will be the number of the
values in the population okay for example
example
so there are 12 automobiles
manufacturing companies
automobile manufacturing companies in
the united states
so listed below is the given the number of
of
patents granted by the united united states
states
government to each company in a recent year
year
so we have the company number of patented
patented
so in this in this information
a sample or a population
in population so what is the arithmetic mean
mean
of a number of patents
five one one plus three eight five plus
two seven five plus two five seven
plus two three four plus two ten plus
ninety seven plus fifty plus thirty six
plus twenty three
plus thirteen so no homogenous
so our population mean is 195.
okay for the sample mean for group data
the sample mean
is the sum of all the sample values
divided by the number of
sample values sample mean is the sum
x or bar x will be the sample mean
and will be the number values in the
sample for example
globe telecom is studying the number of
minutes used monthly
by clients in a particular cell phone
rate plans or a random sample of
12 clients showed the following number
of minutes used last for
last month okay so we have 1991
77 110 94 92 89 100 119
one one 113 eight three minutes
so what is the arithmetic mean number of minutes
minutes used
group for example means so you have to
get for the midpoint
so get the multiplied by the frequency
and then after i know we have used the
total number of the frequency and we
will get the sample mean
okay check that in okay so we have the
frequency this distribution for the vehicle
vehicle
selling prices the information is
repeated below
so determine the arithmetic mean vehicle
selling price
so in millions of million
0.7 is equal to
two e d divided that is a two so
that is zero point six and
zero point six zero point nine one point
two one point three
one point four two point one and two
point four
so it okay so we have solved for the fx
so in frequency multiplied that in 0.6
it takes 4.8
23 times 0.9 20.7
seventeen times one point two twenty
point four
eighteen times one point five is twenty
seven eight times one point eight is
fourteen point four
four times two point one is eight point four
four
two times twenty two point four is four
is one hundred point five so parasol
mean sample mean is one hundred
point five divided that is 80 so we have 1.26
f x x next
so the properties of arithmetic mean
so every set of interval level or ratio
level data has a mean all the values are included
included
in computing the mean a set of data has
unique mean the mean is affected
by unusually large or small data
values the arithmetic mean
is the only measure of central tendency
where the sum of the deviation
of each value from the mean is zero
so next is [Music]
midpoint we're preparing for the
midpoint of the values after they have
been ordered
from the smallest to largest so there's
there are as many values above the
median as below
it in the the data array
so for an even set of values the
median will be the arithmetic average of
the two middle
numbers for example
in properties not in monopoly so there
is a unique
median for each data set it's not
affected by extremely large or
small values and it's therefore a valuable
valuable
measure of central tendency when such
values occur
so it can be computed for ratio level
inter interval level or ordinal level data
data
so it can be computed for an open
ended frequency distribution if the
median does not lie
okay so the age for the sample of five colleges
colleges
so the height of four basketball player
is in each s
are 76 737 80 and
75 so 73 75 76 and 80.
observation that appears most frequently okay
okay
okay next sample
so the data entry that occurs with the
greatest frequency
if no entry is repeated the data set has
no mode
if two entered entries occur with the
same greatest
frequency each entry is a mode
oh by mode you know by modal
okay zero pi point four one point one
zero point four to zero point four
seventy three zero point four eight and
1.1 so
the one base has been getting one point
one so it doesn't move nothing
yeah i'll determine 27 27 27 25 55 55 88 89
89
so one two three one two three so you know
so 27 and 55 sodito
one two three six seven eight nine ten
okay so the annual salaries of an
architect in selected companies
in the philippines are shown below so
what is the model
okay so the relative position of the mean
mean
so panini my young dream so the range is
the difference between the lowest value
and the highest value so the number of
cappuccinos sold at the starbucks
location in the sm caballon city between
4 pm to 7 pm
for example five days last were 20 40 50
starbucks so we have to determine the
mean division
for the number of cappuccinos sold okay so
so
range largest value minus the smallest
value so the largest value is 80 the
smallest is 20.
negative 30 40 minus negative 10
50 minus 50 0 60 minus 50 is
okay so next so here
uh the barrier samantha sommer
determined the number of tropics
citation issued during the last five
so 38 26 13 21 and 22.
divide five is 28 so 38 minus 28 is
positive 10
negative 2 negative 15 positive 13
negative 6.
so the hourly wages for the example of
part-time employees at
home depot coming to one are 200 to 110
to 250 and 300
236 is negative 36 negative 26 negative 16
16
six seven six two five six one nine six and
and
20 over five minus one so we have
one six thirty so you know ating sagorilang
rain x for the standard deviation of
group theta
so this is the formula standard
deviation this is one square
of summation of frequency multiplied
quantity of x
minus the mean raised to the squared all
over n minus one okay
so these are the ibis opinion midpoint
0.6 minus the midpoint negative 0.66
0.9 minus 1.26
is negative 0.36
1.2 minus 1.26 0.06
1.5 minus one point eight is positive
zero point twenty four
it's a positive zero point five f five
four but i mean positive zero point
eighty four
positive one point fourteen so i think meaning
meaning
zero point one two nine six zero point
zero thirty six
zero five seven six zero point two nine
one six zero point seven zero five six
and one point two nine nine six
three and now in baltis multiply nothing
and frequency so eight times zero point
four three five six
three point four four eight it's 23
multiplied zero point one two nine sixty
two point
nine eight zero eight seventeen multiply
zero point zero zero three six zero
point zero
six one two eighteen times zero point
zero five seven six one point zero
three six eight eight times zero point
two nine one six is two point three
three two
eight and four times zero point seven
zero five six two point eight two two
four and then two times one point two
nine nine six
root of frequency frequency multiplied
by a quantity of x minus
mean raised to square root all over n
minus 1.
so we have 15.318 over 80 minus 1
so we have 0.44 here so
okay next so that will be our
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