[August SAT Math] Standard Deviation - ONE Simple Key To ALL The Questions | Everything You Need
Summary
TLDRThis video tutorial simplifies understanding standard deviation for SAT test-takers by focusing on estimation rather than exact calculations. It explains the concept of standard deviation as a measure of data spread and uses graphs to illustrate how to determine if data sets have low, high, or equal standard deviations. The instructor guides viewers through examples and practice questions, emphasizing the importance of recognizing graph patterns to solve SAT problems efficiently.
Takeaways
- 📚 Standard deviation questions on the SAT are about estimating rather than calculating the exact value of standard deviation.
- 🔍 The key to solving standard deviation problems is understanding the definition, which relates to how spread out the data points are.
- 📈 Estimating standard deviation involves comparing the spread of data points in different sets or graphs without needing the exact numerical value.
- 📊 Three main types of data plots are discussed: bell curve, skewed graph, and double top, each indicating a different level of standard deviation.
- 📉 In a bell curve, data points are centered and not spread out, suggesting a low standard deviation.
- 📊 A skewed graph has a tail, indicating a moderate spread and thus a standard deviation that is neither too high nor too low.
- 🔑 The double top graph shows data points spread out across two peaks, indicating a high standard deviation due to the high spread.
- 📝 When comparing two data sets, if the spread of data points is the same, the standard deviations are also the same, regardless of their positions or values.
- 📋 If given a table instead of a graph, create a graph to visualize and estimate the standard deviation based on the spread of data points.
- 📐 The range of data (max - min) can be easily calculated from tables and is not affected by the spread of data points, unlike standard deviation.
- 🎯 Memorizing the shapes of data plots and their corresponding standard deviations can help quickly solve SAT questions without complex calculations.
Q & A
What is the main topic of the video transcript?
-The main topic of the video transcript is understanding and estimating standard deviations on the SAT, including how to approach questions related to standard deviations without calculating the exact value.
What is the definition of standard deviation mentioned in the transcript?
-Standard deviation, as defined in the transcript, refers to how spread out the data points are, indicating the degree of variation in the data set.
Why is it unnecessary to calculate the exact value of standard deviation on the SAT, according to the video?
-On the SAT, it is unnecessary to calculate the exact value of standard deviation because the questions require an estimation of whether the standard deviation is low, high, the same, or different, based on the spread of the data points.
What are the three main types of data plots discussed in the video for estimating standard deviation?
-The three main types of data plots discussed are the bell curve, the skewed graph, and the double top graph, each indicating a different level of spread and thus a different estimated standard deviation.
How does the bell curve indicate the standard deviation of a data set?
-The bell curve indicates a low standard deviation because the data points are centered around one value and not very spread out.
What does the skewed graph suggest about the standard deviation compared to the bell curve?
-The skewed graph suggests a standard deviation that is somewhere in the middle, as it is not as tightly clustered as the bell curve but has a bit more spread due to the tail at the end.
How does the double top graph compare to the bell curve and skewed graph in terms of standard deviation?
-The double top graph indicates the highest standard deviation because the data points are spread out significantly with two separate peaks, showing a high degree of variation.
What is the significance of the range in the context of the video transcript?
-The range, which is the difference between the maximum and minimum values in a data set, is mentioned as a simpler measure than standard deviation. However, the video focuses on standard deviation as the main topic of discussion.
How does the video suggest estimating standard deviation from a table of data?
-The video suggests that if given a table of data without a graph, one should create a graph to visually estimate the spread of the data points and thus the standard deviation.
What is the strategy for solving SAT questions on standard deviation as outlined in the video?
-The strategy involves understanding the definition of standard deviation, recognizing the shapes of data plots (bell curve, skewed graph, double top), and estimating the spread of data points to determine the level of standard deviation without calculating the exact value.
Outlines
📚 Introduction to Standard Deviation on the SAT
This paragraph introduces the concept of standard deviation in the context of the SAT exam. It explains that while standard deviation questions can be easy to identify, they require understanding to solve. The speaker emphasizes that the exact value of standard deviation does not need to be calculated but rather estimated based on the spread of data points. The video promises to teach viewers how to estimate standard deviation and solve related SAT questions by the end of the session. The importance of understanding the definition of standard deviation is highlighted, which refers to the degree of variation or spread of data points.
📈 Understanding Standard Deviation through Graphs
The speaker continues to explain how to estimate standard deviation by analyzing the spread of data points depicted in graphs. Three types of graphs are discussed: the bell curve, the skewed graph, and the double top graph. Each graph type is associated with a different level of spread, which in turn affects the estimated standard deviation. The bell curve represents low spread and thus a low standard deviation, the skewed graph has a moderate spread with a correspondingly moderate standard deviation, and the double top graph indicates a high spread, leading to a high standard deviation. The paragraph encourages memorizing these graph types and their implications for standard deviation to efficiently tackle SAT questions.
🔍 Estimating Standard Deviation with Real SAT Questions
The paragraph delves into applying the understanding of standard deviation to actual SAT questions. It uses a sample question involving pulse rates before and after exercise to demonstrate the concept. The speaker guides the viewers in estimating standard deviation by comparing the spread of data points in dot plots. The before-exercise data forms a bell curve with low spread, indicating a low standard deviation, while the after-exercise data resembles a double top with high spread, suggesting a high standard deviation. The explanation shows how to eliminate incorrect answer choices and identify the correct one based on the comparison of data spread.
📊 Graphing Data from Tables to Determine Standard Deviation
In this paragraph, the speaker addresses how to handle SAT questions that provide data in table form rather than graphically. The strategy involves creating graphs from the table data to visually assess the spread of data points. Two data sets are compared: one resembling a skewed distribution and the other a double top. The speaker illustrates how to graph the data points and use the visual representation to determine which set has a higher standard deviation based on the spread. The paragraph reinforces the idea that understanding the spread of data points is key to estimating standard deviation, regardless of the data presentation format.
Mindmap
Keywords
💡Standard Deviation
💡Estimate
💡Spread
💡Data Points
💡Bell Curve
💡Skewed Graph
💡Double Top
💡Range
💡Dot Plots
💡Mean
Highlights
Standard deviation questions on the SAT can be easily spotted but are not always easy to solve.
Estimating standard deviation on the SAT involves understanding the concept without calculating the exact value.
Standard deviation is defined as a measure of how spread out data points are in a set.
A high standard deviation indicates a greater spread of data points, while a low standard deviation indicates the opposite.
Understanding the definition of standard deviation is crucial for solving SAT questions related to it.
Three main types of data plots are used to estimate standard deviation: bell curve, skewed graph, and double top.
A bell curve indicates a low standard deviation due to data points being centered and not spread out.
A skewed graph has a moderate standard deviation with a slight spread due to a tail at one end.
A double top graph suggests a high standard deviation because of data points being spread out with two peaks.
Memorizing the shapes of data plots and their corresponding standard deviation levels can simplify solving SAT problems.
The video provides a step-by-step guide to estimating standard deviation from different types of graphs.
Practice questions are used to demonstrate how to apply the understanding of standard deviation to SAT questions.
The video explains how to compare standard deviation and range from data plots of before and after an exercise.
The range of data is calculated as the difference between the maximum and minimum values.
When comparing two data sets, if the spread of data points is the same, the standard deviations are also the same.
The mean of a data set is the average value and is affected by the size of the numbers in the set.
If a table is provided instead of a graph, one can estimate standard deviation by graphing the data points.
The video concludes with a summary of the key concepts needed to solve standard deviation questions on the SAT.
Transcripts
what's going guys today we're going to
talk about standard deviations on the
sat
so these questions are very easy to spot
on the sat but they're not very easy to
solve
you're going to see questions like
standard deviations mentioned in the
question
or talk about standard deviation is it
larger or are they the same or is it
impossible to calculate from the
information
given above over here quick tip
usually never the answer and you're also
going to see questions that look
something like this where it gives you
two data plots that look something like
this
and based on the information you have to
find out whether standard deviations are
the same
less than greater than or they're just
flat out different so the thing about
standard deviation on the sat is you
don't need to
calculate what the exact value of
standard deviation
is rather all you need to do is estimate
what understand whether the standard
deviation is going to be low high or
going to be the same or it's going to be
different
and how you can estimate the standard
deviation is exactly what you're going
to learn in this video
by the end of this video you're gonna
know how to solve all four of these
questions so if you're ready to get
started excited to raise your score and
score higher on your next sat
smash the like button and let's get
started with today's video
so as i mentioned all you need to know
how to do
on the sat is estimating standard
deviation
and how do you estimate the standard
deviation well
it's all about understanding the concept
about standard deviation
more importantly you want to understand
the definition of the standard deviation
and what is the definition well standard
deviation is just
simply referring to how spread out
the data points are
how spread out the data points are that
is what standard deviation is
it all depends on how much it's spread
out
okay so if it's spread out a lot
that means your standard deviation is
going to be very high
but if it's not very spread out then
your standard deviation is also going to
be
low as well in other words it's
essentially referring to
the degree of variation
in your data points okay and if this is
confusing right now
don't worry it's going to make more
sense as we go through a couple of
examples and what do i mean by
how spread out these data points are
right well let me give you a couple
examples
we have two data sets a over here and b
over here
and for data set a we see that a lot of
these data points are
clumped around two they're not very
spread out
they are centered around a specific
value
however for data set b okay there is
some clump right there they're kind of
centered towards
two as well but we also have a decent
number of points that are
also away from this peak or clump
right there and by looking at all of
these data points we can tell that oh
for data set b
it's pretty highly spread out compared
to data set a
where it's clumped around this one spot
right there
not much not very spread out but sorta
more spread out than data set a and
because
it's more spread out that tells us that
okay
the standard deviation is also going to
be higher
because standard deviation all it's
referring to is
how spread out the data points are and
because it's more
spread out for data set b we know that
the standard deviation is going to be
higher
for data set b however for data set a
because it's not very spread out it's
rather clumped in just
one spot it's not very spread out which
means our standard deviation is also
going to be lower
as well essentially it's talking about
how spread out
the data points are or also talking
about the degree
of variation among the data points
and that is the connection you want to
learn how to make in order to solve
these standard deviation questions
not much spread that means your standard
deviation is low if the data points are
very spread out that means your standard
deviation is going to be high
if they're spread out evenly that means
their standard deviations
are going to be equal to one another
makes sense
so specifically for the sat you want to
know two things about standard deviation
first one is the definition which is
what we just went over
and second you want to understand how
graphs work there are three main types
and before
we go straight into the graphs make sure
you have understood all of that
because if you don't understand this
graphs are not going to make sense and
it's going to be messy
give yourself a second and try to
understand what just happened maybe
watch a couple more times but
make sure you get the definitions down
before you move on to the graphs
and if you're ready for the graphs let's
talk about the graphs
it's pretty similar this is the first
type second type and the third type
and what you want to understand what to
do with these three graphs over here is
you want to understand how to
estimate the standard deviation based on
the shapes
of these graphs and how can we estimate
the standard deviation
it all goes back to the definition of
standard deviation
which is equal to how spread out
the data points are
okay based on how spread out the data
points are
you can estimate what the standard
deviation would be is it the same is it
the greater or is it going to be less
than
okay so let's go over to these three
graphs and by looking at these graphs
can you tell which one has the highest
standard deviation and which one has the
lowest standard deviation
well let's find out the first type is
going to be
looking like this it's going to be a
bell curve
second type is known as the skewed graph
it's got a little tail at the end
and the third type is known as the
double top where it peaks
at two separate points and
based on the shapes of the graph how can
we estimate what the standard deviation
is
well just focus on how spread out the
data points
are here's what i mean by that if you
look at the bell curve
all the data points are just centered
around this one piece
which makes it a shape of a bell curve
and because
it's centered around this one piece it's
not
very spread out spread is pretty low
which means our standard deviation is
going to be pretty low as well
okay what about skewed graph well skewed
graph
is pretty similar to the bell curve but
it's got a little
tail at the end right here it's kind of
centered
it's not very very spread out but it's
still got
a little bit of spread because of this
tail portion
right here so our standard deviation is
not like
very low but it's not like high either
so it's kind of like
in the middle right and because the
spread
is somewhere in the middle that tells us
that standard deviation is going to be
somewhere in the middle
as well now let's talk about the double
top
double top do these points are
everywhere we have two peaks right there
we have a lot of points
right here and we also have points here
here here here
here the points are not centered in one
spot
like the bell curve or the skewed curve
rather these points have two tops
and data points are spread out pretty
much everywhere okay that tells us that
okay our spread is very high it's not
centered in one spot our spread is very
high
which tells us that our standard
deviation is going to be very high
as well okay so what you need to
understand is
for double top standard deviation is the
highest
and the skewed and the bell curve is
going to be the lowest
okay first you want to understand
why that's the case and second you want
to memorize
these shapes and their orders so that
you can just use them
on the sat without even thinking about
it and that's pretty much all there is
to it as long as you understood
the definition of the standard deviation
and you understood
these graphs not purely memorize them
but understand how
these graphs work every single standard
deviation question on the sat you're
gonna know how to solve
and now we're gonna do about four
practice questions that you have seen in
the beginning
so if you're ready we'll move on but if
you need a second pause the video and
make sure you understand
these two things okay if you're ready
let's go to the practice questions so
let's go over this first question right
here
number 28 which tells us that's going to
be a pretty difficult question because
pretty much toward the end the 22
students in health class conducted an
experiment in which they recorded their
pulse rates and beats per minute
before and after completing a light
exercise routine
the dot plots below display the results
okay so we have beats per minute before
the exercise and the
beats per minute after the exercise okay
we have a student that's
having 88 and a lot of students having
at 72.
okay each of these dots represent
students
the question says let s1 and r1 be the
standard deviation
and the range respectively meaning
standard deviation
is s1 range is r2
of the data before exercise and let s2
and r2 be standard deviation blah blah
of the exercise okay
so ones are going to be before and twos
are going to be the actors which the
following is true right
so what's happening is they're comparing
standard deviation
and the range and range
is pretty simple range is just maximum
minus minimum
right so our range is going to be the
same for two data sets
well let's find out 88 56
is going to be 32 and for after it's
going to be 112
minus 80 which is going to be 32 as well
that means the range is going to be the
same
which means choice b and c are going to
be out
but what about standard deviation are
standard deviations
going to be the same or are they going
to be different
well that's for us to find out and as i
mentioned before you don't need to find
out the exact
value of the standard deviation all you
need to do is estimate
what the standard deviation would be so
how do we estimate it
by using the definition which is talking
about how spread out
the data points are okay if you look at
before
it's in the shape of a bell curve it's
not very spread out
all the data points are pretty much
clumped together towards the middle
which means spread is low which means
your standard deviation is also going to
be low
as well but what about afterward
it kind of looks like a double top
ish right and because it's a double top
it's pretty much like data points are
even like spread out everywhere so our
spread is is very high
which means our standard deviation is
very high so obviously
these two data sets are going to have a
what different
standard deviation so choice a is going
to be up
choice d is going to be the answer makes
sense you see how easy that question was
it's supposed to be one of the hardest
questions on the sat because it's number
28.
but once you know the concept that once
you got the concept down and you know
exactly what to look for in a question
the question just becomes
so much easier that's exactly how sat is
as long as you know what to look for
it becomes that easy let's keep going
next question
so two different data sets are displayed
in the dot plus shown below which is the
following statement is going to be true
so we have a
set a right there and set two right
there
and what are we comparing well it seems
like the mean
of data set one is less than the mean of
data set two
and standard deviation okay so mean
standard deviation
we're comparing mean and the standard
deviation of
two sets right here so mean you can
pretty much calculate on your own
but let's talk about standard deviation
of these two things
and all you need to look at are how
spread out these data points are
and based on the spread you can tell
whether it's going to be high or it's
going to be low
and let's look at data points right here
we see that it's interesting the data
points are
pretty much identical we have three four
and a lot
three four and a lot and one three four
five five five five
so we practically have the same
pattern for these two things the only
difference is that
they are located in different positions
and we know that the standard deviation
is only concerned about
how spread out how spread out these data
points are
and we see that these data points are
spread out the exact
same way because the spread is exactly
the same
we can tell that the standard deviations
are also going to be exactly the same
for these two data sets and some of you
guys
might be wondering but john these data
points are
located in different values wouldn't
that affect
the standard deviation as well well the
thing about standard deviation is that
it doesn't care whether it's in the high
numbers or in the low numbers
all it cares about is not the value of
the numbers
but how spread out these numbers are
and because we are only focused on the
spread of the data points
it really doesn't matter where these
data points are located
so we can tell confidently that standard
deviation is going to be the same
for these two data sets and when it
comes to the mean
what mean is referring to the average
value and
we know that data set two is made up of
bigger numbers
than data set one which means your
average is going to be bigger
for data set two so based on that
the answer is going to be
mean of data set one is less than
but near deviation is greater nope
standard deviation is the same
answer is going to be choice a let's go
to the next question
so this was a little different rather
than giving you a
graph that looks something like that it
just gives you a
ugly looking table right here and how
are we supposed to find out standard
deviation
based on this table well let's keep
going so the table below gives
distribution of high temperatures in
degrees fahrenheit for city a and cdb
for the same 21 days in march
okay instead of giving us nice little
graphs it's giving us
ugly tables and based on that which of
the following is true about the data
shown in 21 days
right and we're talking about standard
deviation deviation deviation
and deviation and it's going to be
larger smaller
or they're going to be the same or these
cannot be
calculated with data provided which is
usually never
the answer so when you are given a
graph like that you can easily tell or
you can easily estimate what the
standard deviation would be
all you have to look at is how spread
out these data points are right it's
pretty simple
but when you're given this table and
you're not given a graph
how are you supposed to estimate it
right well
if you need a graph just graph it out
so i'm going to graph out this data
table right here
we have 76 7 8 9
80. okay right there and we have
1 1 2 14 3 1
1 2 and 14
one two three okay so it looks
something like that somewhat bell curve
somewhat skewed-ish but
let's go to the second one so that's cda
so the b
is going to be looking like same thing
76
7 8 9 80.
and we have six four two three six we
have
one two three four five six four
two three
and six okay so based on that our graph
kind of looks like that
and see how it works out that's let's
just call it
like skewed here and that's going to be
a double top
right and based on what we have learned
double top
is spread out very highly which means
which means your standard deviation
is also going to be very high but for
the skewed curve
not very spread out so your standard
deviation is going to be eh
not very high either so we know that in
in terms of standard deviation b
is going to be greater than a because
data points in b
are more spread out and the choice that
says that is going to be well let's look
at a
standard deviation of temperatures in a
is larger a is larger no that's not true
deviation b is larger b is larger that's
true
they are going to be the same not true
make sense
so when they just give you a table and
you need a graph just graph it out
it makes your life a lot easier so in
summary when it comes to standard
deviation
two things you need to know first is the
definition which is talking about
the spread of the data points high
spread
meaning there's a high standard
deviation and you also want to
understand
how standard deviation works based on
the shapes
of the data points there's the bell
curve there's the skewed curve
and there's also a double top so as long
as you understood
these two things right here every single
standard deviation question on the sat
is going to be very very
easy so if you found this video helpful
give it a thumbs up if you guys have any
questions or comments
leave it in the comment section down
below and i'll see you on the next
video
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