How To Make a Histogram Using a Frequency Distribution Table

00:11:16
https://www.youtube.com/watch?v=AndS0RLdxtk

Summary

TLDRThe video provides a detailed guide on constructing and interpreting histograms using test scores as an example. It starts by explaining the creation of a frequency distribution table, where test scores are grouped into class intervals (ranges of 10, such as 40-49, 50-59, etc.). These intervals help in organizing data effectively for visual representation. The video explains how the histogram, a type of bar chart without spaces between bars, uses the x-axis for grade ranges (independent variables) and the y-axis for frequency (dependent variables) to illustrate how many students fall within each grade range. It further discusses the concept of skewness in data distribution, showing that the sample data is skewed to the left (or negatively skewed). The mode is identified as the range with the highest frequency, which in this case is 80-89. The video concludes with practical questions to help viewers practice interpreting histograms and determining the count of students falling within specified score ranges, emphasizing how to reference ranges such as 'at most 69' and 'at least 80'.

Takeaways

  • 📊 Histograms are visual tools for representing data frequency.
  • 🔢 Test scores are grouped into intervals of 10 for ease of analysis.
  • 📈 The frequency distribution table is a precursor to creating a histogram.
  • 🔄 The x-axis shows the grade ranges, while the y-axis indicates frequency.
  • 📉 The data in this example is skewed to the left (negative skew).
  • 📌 The mode is the interval with the highest frequency.
  • 📚 'At most' and 'at least' signify the inclusivity of the range limits.
  • 🎓 Histograms aid in answering data-related questions effectively.
  • 🧐 Observing histogram shapes can reveal data skewness.
  • 🔍 Understanding histogram components is essential for data interpretation.

Timeline

  • 00:00:00 - 00:05:00

    This video discusses constructing a histogram, starting with organizing test score data into a frequency distribution table. The table groups grades in ranges of 10 (e.g., 40-49, 50-59) to simplify the frequency calculation of student scores. The speaker explains how to tally the frequency for each range: one student scored between 40-49, one between 50-59, two between 60-69, four between 70-79, five between 80-89, and four scored 90 or above. The speaker then describes the process of transferring this frequency data into a histogram, noting the differences between histograms and regular bar graphs, such as the absence of spaces between bars.

  • 00:05:00 - 00:11:16

    The speaker continues by explaining how to construct the histogram based on the frequency data already established. The bars in the histogram represent the frequency of scores within each grade range (e.g., 40-49, 50-59). The video then poses questions related to analyzing the histogram, such as identifying skewness – the data is skewed to the left, indicating a negative skew – and determining the mode, which corresponds to the most frequent score range (80-89). The speaker further demonstrates how to use the histogram to solve common problems, e.g., calculating the number of students scoring at most 69, at least 80, and between 60 and 89 inclusive, illustrating how histograms can be a useful tool in statistical analysis.

Mind Map

Video Q&A

  • How is a histogram constructed?

    A histogram is built using the frequency distribution of the given data. The frequency of each group indicates how many data points fall within that range.

  • What is a frequency distribution table?

    A frequency distribution table organizes data into specified ranges, showing the frequency of data within each range.

  • How are test scores grouped for the histogram?

    In the video, test scores are grouped into ranges of 10, such as 40-49, 50-59, etc.

  • What is the mode in the context of a histogram?

    The mode is the range with the highest frequency in the histogram.

  • Is the data in the histogram symmetric?

    The histogram presented is skewed to the left, indicating a negative skewness.

  • What do the x-axis and y-axis represent in a histogram?

    The x-axis represents grades (independent variables) and the y-axis shows the frequency (dependent variables).

  • How does a histogram differ from a bar graph?

    The histogram has no spaces between bars, indicating continuous data.

  • What do 'at most 69' and 'at least 80' mean?

    In the context of the video, 'at most 69' means a score of 69 or lower, while 'at least 80' means a score of 80 or higher.

  • Why are test scores grouped in intervals of 10?

    Grouping data into class intervals of 10 helps in better visual representation and understanding of the data distribution.

  • How many students scored between 60 and 89 inclusively?

    11 students received a score between 60 and 89 inclusive.

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  • 00:00:01
    in this video we're going to talk about
  • 00:00:02
    how to make a histogram
  • 00:00:05
    and so what we have here is
  • 00:00:08
    the test scores of
  • 00:00:10
    many students in the class
  • 00:00:12
    how can we use this information to
  • 00:00:14
    construct a histogram
  • 00:00:17
    well the first thing we need to do is
  • 00:00:18
    create
  • 00:00:19
    a frequency distribution table
  • 00:00:23
    so we're going to have two columns
  • 00:00:26
    the first one is going to be the grades
  • 00:00:29
    and we're going to arrange this
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    we're going to set up a class with or a
  • 00:00:34
    range of grades
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    we're going to group
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    certain values together
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    and because we're dealing with test
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    scores it makes sense to group it in
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    terms of
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    in ranges of 10.
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    on the right i'm going to put the
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    frequency
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    so the lowest test score that i see is
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    in the 40s
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    the lowest is 42.
  • 00:00:58
    so my lowest range is going to be 40 to
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    49
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    and then the next range will be 50 to
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    59.
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    now sometimes you can calculate the
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    width
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    the class width which in this case is
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    about 10
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    but for grades it's just
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    easy to do it this way we don't really
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    need to calculate it
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    in the u.s a score of 60 to 69
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    usually represents a d
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    70 to 79 represents a c
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    80 to 89 represents a b
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    and 90 or above represents a hundred
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    below 60 it's an f
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    so how many students
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    receive this score
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    between 40 and 49
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    so looking at our data there's only one
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    score in the 40s
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    and that's 42.
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    so the frequency
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    for this range is one
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    only one student had a grade between 40
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    and 49.
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    now what about between 50
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    and 59
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    the only score in that range
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    is 52 so once again the frequency
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    is going to be one
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    now how many students receive a score
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    between 60
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    and 69
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    so let's see we have one
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    two
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    and that's all i have right now
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    so two students received a score between
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    60 and 69.
  • 00:02:37
    now what about in the 70s
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    we have one
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    two
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    three
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    so four students received a grade
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    between 70 and 79
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    now let's move on to the 80s
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    so we have one
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    two
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    three four five
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    so five students scored between 80 and
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    89
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    and then finally we have one
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    two
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    three
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    four students received an a or scored 90
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    or more
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    and so this is our frequency
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    distribution table
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    once we have that set up now we can
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    construct the histogram
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    the histogram looks like a bar graph
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    but the only difference is that
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    the bars
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    are attached to each other there's no
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    spaces between the bars
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    on the y-axis
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    we're going to have the data that
  • 00:03:39
    corresponds to the frequency
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    so these are the independent variables
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    on the x-axis
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    we're going to put the grades which are
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    dead
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    actually i take that back this is the
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    independent variables the grades are the
  • 00:03:54
    independent variables
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    the dependent variables are the
  • 00:03:57
    frequencies
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    the dependent variables are always on
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    the y-axis the independent variables
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    are always on the x-axis
  • 00:04:07
    can't believe i almost mixed that up
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    so now let's
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    continue
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    so we're going to do is we're going to
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    plot these numbers on the x-axis
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    the lowest number is a 40
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    and then it's going to be
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    50
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    and then 60.
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    seventy
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    eighty
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    ninety and the highest is a hundred
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    now for the y values the highest is five
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    so i'm going to go up by one so this is
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    one
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    two
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    three
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    four
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    and five
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    so let's plot the first one
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    let's create a bar that goes up to one
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    so between 40 and 50
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    the frequency is only one
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    now between 50 and 59
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    the frequency is still one
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    and between 60 and 69
  • 00:05:09
    it goes up to two
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    so this one's gonna be a little bit
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    taller
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    and then from 70 to 80
  • 00:05:16
    it goes up to four
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    and then from 80 to 89
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    or just under 90. it goes up to five
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    and from 90 to 100
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    it's four
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    and so that's how we can construct the
  • 00:05:36
    histogram
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    for the data that we have here
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    as you can see it's very straightforward
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    now here's a question for you
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    using the histogram that we have on the
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    board
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    would you say the data
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    is symmetric
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    or would you say it's
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    skewed to the right or skewed to the
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    left
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    what would you say
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    so our data
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    has this type of shape
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    so notice that
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    we have a long tail
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    on the left side
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    so therefore this type of data
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    we could say
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    it's skewed
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    to the left
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    or it has a negative skew
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    it's not skewed to the right and it's
  • 00:06:27
    not symmetric
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    now what is the mode
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    for this particular
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    data
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    the mode is basically the range in this
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    case with the highest frequency
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    so most students receive the score
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    between 80 and 89
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    and so that range would be the frequency
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    i mean the mode for this particular
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    histogram
  • 00:06:56
    now sometimes
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    you might be given a histogram
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    and you need to answer some questions
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    using the histogram and nothing else
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    and so we're going to do that right now
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    so here on the board we have three
  • 00:07:09
    questions
  • 00:07:11
    pause the video
  • 00:07:12
    use the histogram
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    to answer these three questions
  • 00:07:18
    so let's begin
  • 00:07:20
    number one
  • 00:07:21
    how many students
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    received at most
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    a score of 69
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    on the exam
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    so what does that mean
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    at most
  • 00:07:32
    a score of 69
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    is that more than 69 less than 69 does
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    it include 69 what would you say
  • 00:07:40
    so let's write an inequality
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    at most means the maximum score is 69.
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    so using s for the score
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    s has to be less than or equal to 69.
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    it can be up to 69 or less but not more
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    than 69
  • 00:08:02
    so the scores that are below 69 starts
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    here everything
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    to the left of 70.
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    so between 40 and 50
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    we have one student who scored in that
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    region
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    between 50 and 60 is one student
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    and between 60 and 70 but technically
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    between 16 and 69
  • 00:08:23
    we have uh
  • 00:08:25
    not one but two students
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    who scored in that range
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    so the total number of students is going
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    to be one plus one plus two
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    so thus we have four students
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    who received
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    a score of 69 or less on the exam
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    now what about number two
  • 00:08:49
    how many students
  • 00:08:51
    received a score of at least
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    80 on the exam
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    what would you say
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    so what does that mean of at least 80
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    is that less than 80 or more than 80.
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    in this case 80 is the minimum
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    in the last example 69 was the maximum
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    so it has to be
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    80 or more s has to be equal to or
  • 00:09:19
    greater than 80.
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    what we want is the data
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    to the right of this region highlighted
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    in blue
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    so between 80 and 89 we have five
  • 00:09:29
    students
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    who scored in that range
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    and between 90 and 100 there were four
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    students who scored in that range
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    so five plus four is nine
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    and so that's the answer for number two
  • 00:09:45
    now what about the last one
  • 00:09:47
    how many students received a score
  • 00:09:49
    between 60
  • 00:09:51
    and 90.
  • 00:09:53
    well let's adjust this and let's say
  • 00:09:55
    between 60
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    and 89
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    inclusive
  • 00:10:02
    inclusive means that we're going to
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    include
  • 00:10:05
    60 and 89
  • 00:10:09
    because sometimes it may not be
  • 00:10:10
    inclusive
  • 00:10:11
    it may not include 60 to 89 so this
  • 00:10:14
    would be 61 to 88
  • 00:10:16
    but let's say inclusive
  • 00:10:19
    how many students would
  • 00:10:21
    fall in this range
  • 00:10:25
    so our starting point is here 60
  • 00:10:30
    and our ended point is here
  • 00:10:33
    89
  • 00:10:35
    so between 60 and 69 there were two
  • 00:10:37
    students who
  • 00:10:38
    received the score in that range between
  • 00:10:40
    70 and 79 there were four students
  • 00:10:43
    and between 80 and 89 there were five
  • 00:10:47
    so we're gonna add up two plus four
  • 00:10:49
    which is six
  • 00:10:50
    plus five that's 11.
  • 00:10:52
    so 11 students
  • 00:10:55
    received a score between 60 and 89
  • 00:10:58
    inclusive
  • 00:11:00
    and so that's basically it for this
  • 00:11:01
    video
  • 00:11:03
    now you know how to create a frequency
  • 00:11:05
    distribution table
  • 00:11:06
    and you could use that to create a
  • 00:11:08
    histogram
  • 00:11:10
    and now you know how to answer questions
  • 00:11:12
    using a histogram
  • 00:11:14
    thanks for watching
Tags
  • histogram
  • frequency distribution table
  • test scores
  • data grouping
  • histogram skewness
  • x-axis y-axis
  • bar graph