Math 13 Section 1.1

00:12:34
https://www.youtube.com/watch?v=205Q3LN_zPQ

摘要

TLDRIn this video, math instructor Greg Perkins from Hartnell College introduces basic statistical concepts in Math 13, covering definitions, the importance of critical thinking, and the distinction between statistics and parameters. He emphasizes understanding the population versus the sample and warns about biases from non-random samples. Using examples like surveys, data graphs, and stock prices, Perkins illustrates the urgent need for critical analysis when interpreting statistical results. He explains common misconceptions and demonstrates how small inaccuracies can distort interpretations. The video also highlights converting fractions, percentages, and decimals, adding depth to statistical education.

心得

  • 📊 Population vs. Sample: Learn the difference and importance in studies.
  • 🔍 Importance of Random Sampling: Avoid bias in selecting subjects.
  • 📉 Misleading Graphs: Watch out for improper scale representation.
  • 🧠 Critical Thinking: Essential for interpreting survey results.
  • 🤔 Surveys and Extremes: Often capture polarized views only.
  • 🎯 Statistics vs. Parameters: Derived from samples vs. full populations.
  • 📈 Historical Data Analysis: Example with Gallup polls.
  • 🚫 The Concept of Average: Understand different types like mean and median.
  • 📞 Phone Survey Challenges: Low response rates can skew results.
  • 💡 Mathematical Conversions: Know how to convert fractions, decimals, and percentages.

时间轴

  • 00:00:00 - 00:05:00

    Greg Perkins introduces himself as the instructor for Math 13 at Hartnell College. He begins by explaining basic statistical concepts: the entire group being studied is a population, while a subgroup is called a sample, ideally chosen at random. Data from a sample is termed statistics, while data from the whole population is termed a parameter. Perkins emphasizes the importance of critical thinking in sampling, noting biased sampling methods, like voluntary response samples, often lead to biased results. For instance, polling methods that don't capture a broad spectrum can misrepresent opinions, such as the approval ratings of the Catholic population regarding female priests, which could vary based on cultural and geographical differences.

  • 00:05:00 - 00:12:34

    Perkins discusses the reliability of the Gallup poll regarding congressional job approval, asserting it is generally trustworthy. He highlights analyzing information critically, like questioning the accuracy of statements and statistics, citing examples like predicting class performance and stock price representations. For instance, he critiques a graph showing Apple stock prices: the depiction can mislead if the y-axis doesn't start at zero, exaggerating changes visually. He also discusses potential biases in surveys, like asking about gas prices via phone calls, which can suffer low response rates, and delves into the vagueness of the term 'average' in statistics, explaining different measures like mean, median, and midrange, stressing clarity. Lastly, he covers converting between fractions, decimals, and percentages, showing calculations for percentage and fraction equivalents.

思维导图

Mind Map

常见问题

  • What is a population in statistics?

    A population in statistics refers to the total group that is being studied, such as all people in the United States.

  • What defines a sample in a statistical study?

    A sample in statistics is a subgroup of the population that is chosen for a particular study, ideally selected at random.

  • Why is random sampling important?

    Random sampling is important to avoid bias and ensure that the sample accurately represents the entire population.

  • What is the difference between statistics and parameters?

    Statistics are derived from a sample, while parameters are values obtained from analyzing the entire population.

  • Why are extreme opinions more likely to be reflected in surveys?

    Surveys often reflect extreme opinions because those with strong feelings are more likely to respond, whereas those with neutral views may not participate.

  • Is it reliable to base conclusions on non-random samples?

    No, non-random samples can lead to misleading conclusions as they may not represent the population accurately.

  • What are potential issues with the portrayal of data in graphs?

    Graphs can mislead viewers if the scales are not appropriately set, as it may exaggerate or downplay changes in data.

  • How can statistical misinterpretation occur with statements about averages?

    The term 'average' can lead to misinterpretation if it's not specified whether it refers to the mean, median, mode, or mid-range.

  • What are the critical thinking points regarding survey reliability?

    Critical thinking involves questioning the origins of the survey data, how the sample was selected, and whether it truly represents the population.

  • Why might phone survey results be unreliable?

    Phone surveys might be unreliable due to low response rates, misunderstandings, or quick guesses by respondents.

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  • 00:00:00
    hi my name is greg perkins i am the
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    instructor for this class math 13 at
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    hartnell college
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    section 1.1 is pretty basic got a few
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    definitions
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    and then some critical thinking
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    first of all the total group that is to
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    be studied
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    that is called the population so if you
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    wanted to
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    study the whole united states all the
  • 00:00:25
    people in the united states
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    then that would be some 315 or 318
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    million people that would be a lot but
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    that would be the population
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    of course since that's a lot of people
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    you may want to just go out and
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    interview 70 people throughout the
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    united states
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    well any subgroup like that is called
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    the sample
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    and it's best if you choose the sample
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    at random
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    don't just interview your friends you
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    gotta go out go out and meet some
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    strangers
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    now when you collect data from the
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    sample how tall are you what's your age
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    how much money do you make who did you
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    vote for
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    that type of information when it comes
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    from a sample that's called
  • 00:01:06
    statistics if you do the same thing
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    for the whole population that's called
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    parameter and i remember it because
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    s starts with sample statistic starts
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    with sample
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    parameter starts with p population
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    starts with p
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    so you might figure find out their hair
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    color age
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    their weight how many cars do they own
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    something like that
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    so one part of the critical thinking is
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    people should not be able to choose
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    to join a sample
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    so for example people are asked to text
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    the word either yes or no to some number
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    to indicate whether they liked a movie
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    so what's wrong with this most people
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    aren't going to do it
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    most people are like yeah i don't have
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    the time
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    the people that feel very strongly yes i
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    loved that movie that character with the
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    red hair with a little bit of gray
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    he was awesome well
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    or the people that really don't like it
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    at all
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    so basically you're just going to get
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    the extremes
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    look for example at amazon ratings
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    so i don't even remember what this was
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    for but something
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    so who's going to take the time to go
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    and rate it
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    basically those people that really like
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    it or those people that really don't
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    like it
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    if it's an average customer and they're
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    like yeah it's toothpaste
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    it works fine are they going to go take
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    the time to go and rate it
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    no mostly those people that have the
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    strongest opinions would take the time
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    to go and rate it
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    then just think critically about this
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    suppose that there's this quote
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    50 of catholics say they would be in
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    favor of having female priests
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    so what's wrong with this statement
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    now with this i'm not talking about
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    should the catholic
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    church have female priests or not but
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    just think critically
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    50 of catholics well there are catholics
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    all throughout the world so did they
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    interview people from all throughout the
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    world
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    because perhaps people in the
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    philippines
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    and people in
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    italy people in the united states
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    because of the cultural differences
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    they might have different answers which
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    actually has nothing to do with
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    catholicism
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    so basically just think critically where
  • 00:03:36
    did this come from
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    who are these catholics and did they
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    talk to
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    men and women boys and girls who did
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    they talk to
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    so take a look at this graph does it
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    seem reliable
  • 00:03:52
    so this is con congressional job
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    approval
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    so the question they asked was do you
  • 00:03:58
    approve or disapprove of the way
  • 00:04:00
    congress is handling its job
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    and this is going back from 1974 all the
  • 00:04:05
    way to 2020
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    so does it seem reliable well this comes
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    from gallup
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    and i know that the gallup polls have
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    been around for many many years
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    and i personally think that yeah
  • 00:04:19
    gallop is a reliable source
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    also i look for like right over here
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    would be
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    2001 2002 and then they said congress is
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    doing a great job 84
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    so that was after 9 11 shortly after 9
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    11
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    then people were thinking congress is
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    doing a good job
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    more recently nine percent approval in
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    about 2013
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    and 21 approval in about 2020.
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    so to me yes this does seem reliable
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    and it looks like over here they used to
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    have long gaps
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    when they would between the times when
  • 00:04:58
    they asked the question
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    and here you can see they're asking more
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    and more frequently
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    back in 1985 they probably had to go
  • 00:05:06
    outside and talk to a human being
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    over here perhaps they are calling
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    people
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    or maybe they're still talking human
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    beings i don't know but i do find it
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    reliable now is it 100
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    accurate i doubt it but it seems like a
  • 00:05:24
    reliable source of information
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    next up just categorize in your opinion
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    does it seem possible
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    likely or impossible part a it will rain
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    tomorrow
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    well in california it doesn't rain very
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    much anymore
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    so i would say it's possible
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    but not very likely at all so maybe i
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    should have had not likely in there also
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    so out of the choices i would say
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    possible but i think it's unlikely it's
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    going to rain tomorrow
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    in california part b justin bieber will
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    be the president of the united states
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    someday
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    that is impossible not because of
  • 00:06:03
    politics but because he's canadian
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    yep so can't be a canadian citizen
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    and then be the president of the united
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    states
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    so what are some problems in here i
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    claim that 80
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    of the class will pass with a c or
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    better
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    what if i claim that 80.4 of all my
  • 00:06:26
    previous students have passed with a c
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    or better
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    so if i claim that 80 of the class will
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    pass
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    i'm trying to predict the future so
  • 00:06:38
    if you've seen the way that i pick
  • 00:06:39
    stocks you can tell that i don't know
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    how to predict the future
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    so the first one is trying to predict
  • 00:06:44
    the future and
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    i don't know what you're basing that
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    first statement on
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    okay move on to the second one i claimed
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    that
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    of my previous students so now that's
  • 00:06:54
    something that really did happen in the
  • 00:06:56
    past
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    and look at i'm being more accurate
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    because i'm saying 80.4 percent
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    so that makes it look like i got out my
  • 00:07:04
    calculator
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    and i added up all the students that got
  • 00:07:07
    c's or better total
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    all the students over the last 28 years
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    and then divided and i got 80.4 percent
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    actually it's a pretty good estimate but
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    i didn't actually
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    calculate the numbers but it is around
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    eighty percent that'll pass the class
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    but by putting that point four is just a
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    little bit tiny
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    of a deception just trying to say oh
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    look at how accurate i am i know how to
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    use a 0.4
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    so that's some critical thinking there
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    okay now look at the stock prices
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    so if you go to september 2019
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    apple stock price was 54. september 2020
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    110. now that is truthful information i
  • 00:07:55
    did actually look that up but look at
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    the graph
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    is that an accurate portrayal of the
  • 00:08:01
    information
  • 00:08:03
    well if you take a 54 and double it
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    it would be a 108. so this price right
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    here
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    is approximately double this price but
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    if you look at the bars
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    is this one or excuse me is this bigger
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    one
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    two times bigger than this one now to me
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    it looks like it's
  • 00:08:23
    it looks like the tall one is about
  • 00:08:25
    three times bigger
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    and the problem is over here i should
  • 00:08:29
    have started the scale at zero
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    so i started at 40 which then
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    makes this look disproportionate
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    so if somebody if somebody was just
  • 00:08:41
    looking at the graph they would go
  • 00:08:42
    oh wow it like tripled in price but
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    actually
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    it doubled in price
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    suppose you call someone's house as a
  • 00:08:56
    part of a survey
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    and you ask how much they pay for gas is
  • 00:08:59
    there anything wrong with that
  • 00:09:01
    so for one thing if you call somebody
  • 00:09:06
    oh my gosh i just showed how old i am
  • 00:09:09
    called someone's house how do you know
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    everybody has a phone with them wherever
  • 00:09:13
    they go how do you know they're at their
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    house
  • 00:09:16
    okay it used to be we had landlines and
  • 00:09:18
    the landlines are in the house
  • 00:09:20
    anyway is and you're asking how much
  • 00:09:23
    they pay for gas anything wrong with
  • 00:09:25
    this well
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    for one um a lot of people will not
  • 00:09:30
    answer a phone a phone call from a
  • 00:09:32
    stranger's number so you might have a
  • 00:09:34
    hard time getting people to even answer
  • 00:09:36
    the
  • 00:09:36
    the phone in the first place you ask
  • 00:09:39
    some stranger
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    calls you and asks how much you pay for
  • 00:09:42
    gas you're probably going to hang up on
  • 00:09:43
    them
  • 00:09:45
    then even if you get the person to talk
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    to you
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    how much do they pay for gas so
  • 00:09:51
    [Music]
  • 00:09:54
    three dollars three dollars and 10 cents
  • 00:09:59
    i think that i think i paid 309 the last
  • 00:10:02
    time
  • 00:10:03
    i filled up my tank so the people might
  • 00:10:06
    not even know
  • 00:10:07
    and then they just guess a number
  • 00:10:12
    next up your test scores are 65 70 78 83
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    and 100 is 80 above average
  • 00:10:21
    the problem with this is the word
  • 00:10:23
    average
  • 00:10:24
    is sort of vague we haven't covered this
  • 00:10:26
    yet but we will soon
  • 00:10:28
    for average there's the mean the median
  • 00:10:31
    the mode and the mid-range are all types
  • 00:10:33
    of averages
  • 00:10:34
    so when you say the word average which
  • 00:10:36
    one are you talking about
  • 00:10:38
    the mean would mean that you add up the
  • 00:10:41
    five numbers
  • 00:10:42
    and divide by five the median would be
  • 00:10:46
    the middle number
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    so the middle number is 78 in that case
  • 00:10:51
    if you're talking about the median
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    yeah 80 is above the median
  • 00:10:58
    finally just a little bit of work with
  • 00:11:00
    some fractions percents and decimals
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    so if you take a calculator and go 2
  • 00:11:05
    divided by 5 it's going to tell you a
  • 00:11:08
    0.4
  • 00:11:10
    or 0.40 and then if you move the decimal
  • 00:11:13
    over two places
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    that means forty percent so there's the
  • 00:11:17
    fraction
  • 00:11:18
    the decimal and the percent form all of
  • 00:11:21
    the same number
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    so for eighty-eight percent that's the
  • 00:11:28
    same well actually the word
  • 00:11:29
    per cent is saying per 100
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    because cent means hundreds so per 100
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    so this is actually saying 88 per 100
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    so 88 per 100 means you divide by 100
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    and you could reduce that to 22 over 25
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    so just divide by 4 on the top and
  • 00:11:47
    divide by 4 on the bottom
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    and then fill out this table
  • 00:11:55
    so a 0.9 if you move the decimal two
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    places to the right
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    that's going to be 90 and that means the
  • 00:12:01
    fraction would be 90 over 100.
  • 00:12:05
    whoops sorry about that hit the wrong
  • 00:12:07
    button
  • 00:12:08
    so this one would be 90 over 100 24
  • 00:12:12
    that would be 0.24 and the fraction
  • 00:12:15
    would be 24 over 100
  • 00:12:18
    one half when you divide it that's a 0.5
  • 00:12:22
    and one half means 50
  • 00:12:25
    and finally two-thirds that would be
  • 00:12:27
    0.667
  • 00:12:29
    or 66.7 percent
标签
  • statistics
  • population
  • sample
  • critical thinking
  • survey data
  • bias
  • parameter
  • graph interpretation
  • statistical analysis
  • math education