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.

How To Make a Histogram Using a Frequency Distribution Table

00:11:16

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

Zusammenfassung

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'.

Mitbringsel

📊 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.

Zeitleiste

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

Häufig gestellte Fragen

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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Untertitel

Automatisches Blättern:

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
00:00:33
we're going to set up a class with or a
00:00:34
range of grades
00:00:36
we're going to group
00:00:38
certain values together
00:00:40
and because we're dealing with test
00:00:41
scores it makes sense to group it in
00:00:43
terms of
00:00:44
in ranges of 10.
00:00:47
on the right i'm going to put the
00:00:49
frequency
00:00:52
so the lowest test score that i see is
00:00:54
in the 40s
00:00:56
the lowest is 42.
00:00:58
so my lowest range is going to be 40 to
00:01:01
49
00:01:04
and then the next range will be 50 to
00:01:06
59.
00:01:08
now sometimes you can calculate the
00:01:10
width
00:01:12
the class width which in this case is
00:01:14
about 10
00:01:15
but for grades it's just
00:01:17
easy to do it this way we don't really
00:01:19
need to calculate it
00:01:24
in the u.s a score of 60 to 69
00:01:28
usually represents a d
00:01:31
70 to 79 represents a c
00:01:34
80 to 89 represents a b
00:01:37
and 90 or above represents a hundred
00:01:39
below 60 it's an f
00:01:42
so how many students
00:01:45
receive this score
00:01:46
between 40 and 49
00:01:50
so looking at our data there's only one
00:01:52
score in the 40s
00:01:54
and that's 42.
00:01:56
so the frequency
00:01:57
for this range is one
00:01:59
only one student had a grade between 40
00:02:02
and 49.
00:02:04
now what about between 50
00:02:06
and 59
00:02:09
the only score in that range
00:02:11
is 52 so once again the frequency
00:02:14
is going to be one
00:02:17
now how many students receive a score
00:02:19
between 60
00:02:21
and 69
00:02:24
so let's see we have one
00:02:28
two
00:02:29
and that's all i have right now
00:02:32
so two students received a score between
00:02:35
60 and 69.
00:02:37
now what about in the 70s
00:02:40
we have one
00:02:42
two
00:02:42
three
00:02:44
so four students received a grade
00:02:46
between 70 and 79
00:02:50
now let's move on to the 80s
00:02:53
so we have one
00:02:54
two
00:02:56
three four five
00:02:58
so five students scored between 80 and
00:03:01
89
00:03:04
and then finally we have one
00:03:06
two
00:03:07
three
00:03:08
four students received an a or scored 90
00:03:11
or more
00:03:14
and so this is our frequency
00:03:16
distribution table
00:03:18
once we have that set up now we can
00:03:21
construct the histogram
00:03:24
the histogram looks like a bar graph
00:03:27
but the only difference is that
00:03:28
the bars
00:03:30
are attached to each other there's no
00:03:31
spaces between the bars
00:03:35
on the y-axis
00:03:37
we're going to have the data that
00:03:39
corresponds to the frequency
00:03:41
so these are the independent variables
00:03:44
on the x-axis
00:03:47
we're going to put the grades which are
00:03:50
dead
00:03:51
actually i take that back this is the
00:03:53
independent variables the grades are the
00:03:54
independent variables
00:03:55
the dependent variables are the
00:03:57
frequencies
00:03:59
the dependent variables are always on
00:04:01
the y-axis the independent variables
00:04:04
are always on the x-axis
00:04:07
can't believe i almost mixed that up
00:04:11
so now let's
00:04:12
continue
00:04:14
so we're going to do is we're going to
00:04:16
plot these numbers on the x-axis
00:04:18
the lowest number is a 40
00:04:21
and then it's going to be
00:04:22
50
00:04:24
and then 60.
00:04:28
seventy
00:04:30
eighty
00:04:32
ninety and the highest is a hundred
00:04:36
now for the y values the highest is five
00:04:39
so i'm going to go up by one so this is
00:04:41
one
00:04:42
two
00:04:43
three
00:04:44
four
00:04:45
and five
00:04:48
so let's plot the first one
00:04:51
let's create a bar that goes up to one
00:04:54
so between 40 and 50
00:04:57
the frequency is only one
00:05:00
now between 50 and 59
00:05:04
the frequency is still one
00:05:07
and between 60 and 69
00:05:09
it goes up to two
00:05:11
so this one's gonna be a little bit
00:05:12
taller
00:05:14
and then from 70 to 80
00:05:16
it goes up to four
00:05:21
and then from 80 to 89
00:05:25
or just under 90. it goes up to five
00:05:29
and from 90 to 100
00:05:32
it's four
00:05:34
and so that's how we can construct the
00:05:36
histogram
00:05:37
for the data that we have here
00:05:40
as you can see it's very straightforward
00:05:44
now here's a question for you
00:05:48
using the histogram that we have on the
00:05:50
board
00:05:51
would you say the data
00:05:53
is symmetric
00:05:54
or would you say it's
00:05:56
skewed to the right or skewed to the
00:05:58
left
00:05:59
what would you say
00:06:03
so our data
00:06:04
has this type of shape
00:06:07
so notice that
00:06:09
we have a long tail
00:06:11
on the left side
00:06:13
so therefore this type of data
00:06:16
we could say
00:06:17
it's skewed
00:06:18
to the left
00:06:20
or it has a negative skew
00:06:25
it's not skewed to the right and it's
00:06:27
not symmetric
00:06:30
now what is the mode
00:06:32
for this particular
00:06:35
data
00:06:38
the mode is basically the range in this
00:06:40
case with the highest frequency
00:06:43
so most students receive the score
00:06:46
between 80 and 89
00:06:49
and so that range would be the frequency
00:06:51
i mean the mode for this particular
00:06:53
histogram
00:06:56
now sometimes
00:06:57
you might be given a histogram
00:07:00
and you need to answer some questions
00:07:02
using the histogram and nothing else
00:07:05
and so we're going to do that right now
00:07:07
so here on the board we have three
00:07:09
questions
00:07:11
pause the video
00:07:12
use the histogram
00:07:14
to answer these three questions
00:07:18
so let's begin
00:07:20
number one
00:07:21
how many students
00:07:23
received at most
00:07:25
a score of 69
00:07:27
on the exam
00:07:29
so what does that mean
00:07:31
at most
00:07:32
a score of 69
00:07:34
is that more than 69 less than 69 does
00:07:37
it include 69 what would you say
00:07:40
so let's write an inequality
00:07:44
at most means the maximum score is 69.
00:07:48
so using s for the score
00:07:50
s has to be less than or equal to 69.
00:07:54
it can be up to 69 or less but not more
00:07:57
than 69
00:08:02
so the scores that are below 69 starts
00:08:05
here everything
00:08:06
to the left of 70.
00:08:10
so between 40 and 50
00:08:13
we have one student who scored in that
00:08:14
region
00:08:16
between 50 and 60 is one student
00:08:18
and between 60 and 70 but technically
00:08:21
between 16 and 69
00:08:23
we have uh
00:08:25
not one but two students
00:08:28
who scored in that range
00:08:30
so the total number of students is going
00:08:32
to be one plus one plus two
00:08:34
so thus we have four students
00:08:37
who received
00:08:39
a score of 69 or less on the exam
00:08:45
now what about number two
00:08:49
how many students
00:08:51
received a score of at least
00:08:54
80 on the exam
00:08:58
what would you say
00:09:02
so what does that mean of at least 80
00:09:05
is that less than 80 or more than 80.
00:09:09
in this case 80 is the minimum
00:09:11
in the last example 69 was the maximum
00:09:14
so it has to be
00:09:16
80 or more s has to be equal to or
00:09:19
greater than 80.
00:09:21
what we want is the data
00:09:23
to the right of this region highlighted
00:09:25
in blue
00:09:27
so between 80 and 89 we have five
00:09:29
students
00:09:31
who scored in that range
00:09:32
and between 90 and 100 there were four
00:09:35
students who scored in that range
00:09:38
so five plus four is nine
00:09:41
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
00:09:57
and 89
00:09:59
inclusive
00:10:02
inclusive means that we're going to
00:10:04
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