[August SAT Math] Standard Deviation - ONE Simple Key To ALL The Questions | Everything You Need

Summary

This 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

00:00

📚 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.

05:02

📈 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.

10:03

🔍 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.

15:05

📊 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.

Keywords

💡Standard Deviation

Standard deviation is a measure of the amount of variation or dispersion in a set of values. In the context of the video, it refers to how spread out the data points are in a given dataset. A high standard deviation indicates that the data points are dispersed widely, while a low standard deviation means they are closer to the mean. The video emphasizes that understanding standard deviation is crucial for solving questions on the SAT, where one must estimate the spread without calculating the exact value.

💡Estimate

In the script, 'estimate' is used to describe the process of roughly calculating or judging the value of standard deviation based on the spread of data points. It is a key concept because the SAT does not require the exact value of standard deviation but rather an understanding of its relative magnitude. For example, the video mentions that one should estimate whether the standard deviation is high, low, or the same between two data sets.

💡Spread

The term 'spread' is used to describe the distribution of data points around the mean or central value. In the video, it is directly related to the concept of standard deviation, as a greater spread indicates a higher standard deviation and vice versa. The script uses the term to help viewers understand how to visually assess the dispersion of data points in graphs and tables.

💡Data Points

Data points are the individual values in a dataset that are being analyzed for their distribution and variability. The script frequently refers to data points to illustrate how they can be spread out or clumped together, which affects the standard deviation. For instance, the video uses data points to demonstrate the difference in spread between a bell curve and a double top graph.

💡Bell Curve

A bell curve, also known as a normal distribution, is a type of graph that is symmetric and bell-shaped, with data points concentrated in the middle and tapering off towards the ends. In the video, the bell curve is used as an example of a graph with a low standard deviation because the data points are not spread out widely.

💡Skewed Graph

A skewed graph is one where the distribution of data points is not symmetric, often with a tail extending in one direction. The video mentions the skewed graph as having a standard deviation that is in the middle range, not as low as the bell curve but not as high as the double top, due to its somewhat spread out data points.

💡Double Top

The 'double top' graph is characterized by having two distinct peaks, indicating that the data points are spread out across two different values. The video uses this term to describe a scenario where the standard deviation would be high because the data points are widely dispersed.

💡Range

The range of a dataset is the difference between the maximum and minimum values. While the video's primary focus is on standard deviation, the range is also mentioned as a simple measure of dispersion. The script uses the range to illustrate that even if two datasets have the same range, their standard deviations can differ due to the spread of data points.

💡Dot Plots

Dot plots are a type of graph used to display data by plotting a dot for each data point along an axis. In the script, dot plots are used to visually represent the distribution of data points and to facilitate the estimation of standard deviation by showing the spread of the data.

💡Mean

The mean, often referred to as the average, is the sum of all data points divided by the number of points. While the video's main theme revolves around standard deviation, the mean is also discussed in the context of comparing data sets. For example, the script mentions that the mean of one data set can be less than another, which is a separate concept from standard deviation.

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