histogram assignment answer key

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Our collection of histogram worksheets helps students learn how to read and create this type of graph. Using given data, students can fill in histograms on their own and answer questions interpreting them.

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Here you will learn about a histogram, including how to create a histogram and how to interpret it.

Students will first learn about a histogram as part of statistics and probability in 6 th grade.

What is a histogram?

A histogram is a graphical representation used to display quantitative continuous data (numeric data).

To do this, you need to use the number of observations and the range of values to decide a bin size and the number of bins needed to include all data points.

Sometimes this information is already given to you.

For example,

The table below shows the heights (cm) of plants in a garden.

The bin size is 5 – each group has a range of 5. The values given for the beginning and end of the bin will be used on the x -axis.

There are 4 bins – there are 4 frequencies. Each bin will be drawn as a different bar, so this graph will have 4 bars. The height of each bar is the frequency, which is labeled on the y -axis.

One important benefit of a histogram, is that it can be used to show the frequency distribution shape of a data set.

Let’s explore this further by comparing the visualizations of a few histograms.

The histogram above falls within what is called a normal distribution. Notice how the data is evenly centered and consistently decreases on both sides of the center. This causes a symmetric shape.

Notice how the two histograms above look different from the one that has a normal distribution. The distribution of data in these sets is NOT symmetric. Both have skewness. This can be caused by outliers or other factors, but skewness means that the data “leans” to the left or to the right.

Finding the median bin

While it is impossible to know the exact range or mean of the data set when only given the histogram, you can identify in which bin the median lies.

Consider the number of data points in each bin.

The bins of the histogram are already in order from smallest to largest. This means the first bin (135-140) has the 7 smallest data points – shown in red. The larger bins (155-160, 150-155 and 145-150) have the 7 largest data points – shown in green.

Notice that the 7 largest will include 2 from the middle bin (145-150).

Continuing inward to find the median, if you take the 3 remaining data points in 145-150 and the smallest 3 remaining data points in 144-150, there would still be 3 data points in 140-145. This means the middle data point lies in this bin.

It is important to note that the exact median is NOT known, just what bin it belongs to.

Note: The class intervals (bin width) shown on this page will be equivalent, but this is not a requirement for histograms. In higher level mathematics courses, students explore histograms with varied bin sizes and frequency density.

Common Core State Standards

How does this relate to 6 th grade math?

• Grade 6 – Statistics and Probability (6.SP.B.4) Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

How to create a histogram

In order to create a histogram:

Decide what bin size to use and how many bins are needed.

Group the data by the bin sizes to find the frequency.

Create bars based on the bin sizes and frequencies within the bins.

Label the \textbf{x} and \textbf{y} axes with units.

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Histogram examples

Example 1: creating a histogram from grouped data.

The table shows information about the ages of people at a park.

Use the information in the table to create a histogram.

In this case the data is already given to us in intervals, which will serve as the bin size.

2 Group the data by the bin sizes to find the frequency.

In this case the frequency of each bin is given.

3 Create bars based on the bin sizes and frequencies within the bins.

4 Label the \textbf{x} and \textbf{y} axes with units.

Example 2: creating a histogram from listed data

Create a histogram for a data set of tree heights (meters):

1.2, \, 2.3, \, 1.1, \, 1.2, \, 3.5, \, 4.5, \, 3.4, \, 2.3, \, 2, \, 3.3, \, 4.1, \, 2.3, \, 1.1, \, 5.6

The smallest data point is 1.1 and the largest is 5.6. Let’s use a bin size of 1.

*Note: 1 is not the only option. You can use any bin size that includes all values.

Example 3: creating a histogram from listed data

Create a histogram for a data set of test scores:

67, \, 79, \, 91, \, 93, \, 86, \, 74, \, 60, \, 78, \, 92, \, 88, \, 85, \, 90, \, 83, 79, \, 95, \, 66, \, 81, \, 80, \, 84

The smallest data point is 60 and the largest is 95. Let’s use a bin size of 6.

*Note: 6 is not the only option. You can use any bin size that includes all values.

How to interpret a histogram

In order to interpret a histogram:

Find the bin that has the median.

Describe the center and spread of the histogram within the context.

Example 4: interpreting center and spread of a histogram

Consider the following histogram. State the bin where the median lies and describe the center and spread of the data within context.

The first bin (0-2) has the 30 smallest values. The other bins have 25 values in all, which is less than half. This means the median value is in the first bin.

Over half of the data set (including the median) is in the first bin. The data overall is right-skewed, with most of the data falling within the first two bins. The value in the last bin (6-8) could be an outlier, since it is so far from the center of the data.

Considering the context, we can say that over half of the people have 0 or 1 dog and most of the people have less than 4 dogs.

Example 5: interpreting center and spread of a histogram

One way to find the median is to start with the lowest and highest bin and add a cross for each data point in the bin, working your way to the very middle. This is similar to finding the median of a set of numbers.

Most of the customers spent between \$15 and \$30. There was one customer who spent from \$45-\$50, which seems to be an outlier.

The data are somewhat symmetrical around the median, but there are a few more data points in the bins to the right of the median bin.

Example 6: interpreting center and spread of a histogram

One way to find the median bin is to list out the bins, considering their frequency, in order from least to greatest.

The data set is even, so there are two data points (in this case their bins) in the middle. Since they are the same, we know that the median lies in the 0.4-0.5 bin.

There is no symmetry around the median in this histogram. It is a little right-skewed, but not much. After the first two bins, which are the two largest, the bins are very similar.

Teaching tips for histogram

• Creating a histogram requires many steps, so provide students with links to tutorials or the steps written out to refer to as they are learning how to create them.
• Utilize interactive programs like excel to allow students to spend time exploring how changing the bin size for a set of data affects the distribution of the data and therefore affecting the conclusions that might be drawn.
• It is important that students spend time creating histograms and analyzing them, instead of prioritizing one skill over another. The act of creating a histogram helps students analyze them, since they know how the data was grouped. Analyzing histograms helps students think critically when creating them, particularly when considering what bin size is appropriate or what conclusions can or cannot be drawn based on how the data is displayed.

Easy mistakes to make

• Labeling the horizontal axis as discrete groups, rather than a continuous scale The horizontal axis of a bar chart is divided into discrete categorical variables with gaps between the bars. Sometimes this knowledge is incorrectly transferred to histograms. A histogram plots values on a continuous scale, so there are no gaps between the bins.

• Thinking there is only one “correct” bin size When representing a set of data as a histogram, there is usually more than one appropriate bin size. Many programs that generate histograms have algorithms that automatically generate a bin size, but that does not automatically mean that the calculated bin size is the most appropriate. It is important to consider the context of the data and the purpose of the analysis.

Related frequency graph lessons

• Frequency graph
• Frequency distribution
• Cumulative frequency
• Frequency polygon

Practice histogram questions

1) Which histogram shows the data in the table?

The number of birds is from 0-40 and shown on the x -axis. The number of days is from 9-75 and is shown on the y -axis. A histogram displays continuous data, so the bars are always connected.

2) Data set (total visitors per day):

120, \, 123, \, 122, \, 172, \, 168, \, 121, \, 145, \, 191, \, 177, \, 155, \,  120, \, 155

Which histogram shows the data set above?

Organizing the data points from least to greatest in these groups:

120, \, 120, \, 121, \, 122, \, 123

145, \, 155, \, 155

168, \, 172, \, 177

Creates the following frequency table:

This is graphed with the number of visitors on the x -axis and number of days on the y -axis.

3) Data set (total points per game):

15, \, 17, \, 3, \, 22, \, 25, \, 33, \, 10, \, 7, \, 21, \, 33, \,  37, \, 15, \, 10, \, 9

7, \, 9, \, 10, \, 10,

15, \, 15, \, 17,

21, \, 22, \, 25,

This is graphed with the number of points on the x -axis and number of games on the y -axis.

In which bin is the median in the histogram above?

In the histogram above, which bin contains the median?

The first bin and 1 value from the second bin have the 8 smallest values.

The third and fourth bin, plus 3 values from the second bin have the 8 largest values. This leaves 1 value in the second bin (0.8-1.2) which will be the median.

Which statement describing the spread of the histogram above is NOT true?

The bins smaller than the median have the least variation.

The data is left-skewed.

The largest bin is almost double the next largest bin.

The three largest bins are to the right of the median bin.

The median is in the bin (6-7.5), which is the second largest bin.

This means the largest bin is to the right of the median bin and the median bin is the second largest bin. So, the three largest bins are NOT to the right of the median bin.

Histogram FAQs

Other graphs that can show how data is distributed are pie charts, which also group data into groups – but are not necessarily continuous. Line graphs can show how continuous data changes over time. Box plots group continuous data into a 5 number summary.

A bar chart (or bar graph) is used to display qualitative or quantitative discrete data – which is why the bars do not touch. It does not necessarily have numeric data, whereas a histogram always has continuous, numeric data – which is why the bars touch.

The next lessons are

• Sampling methods
• Probability
• Compound probability
• Units of measurement
• Represent and interpret data

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Reading Histograms Worksheets

Basic Lesson

Using a snap shot of random data, students learn to read histograms. The discounts offered by super market are shown in the table. Represent the data in the histogram. 1. Set up the bottom axis (x axis- Amount). Look at total range of values and check the lowest value. Plot the range of values on axis. 2. Set up side axis (Y axisDiscount). Group up the values on the similar range of X axis (Amount). 3. Construct data bars centered over X axis.

Intermediate Lesson

Students begin to read large histograms.

Independent Practice 1

Students interpret 20 histograms.

Independent Practice 2

Students interpret another 20 histograms.

Homework Worksheet

Offers 12 questions for home and provides an example.

Students use a series of histograms to answer 10 quiz questions.

Homework and Quiz Answer Key

Answers for the homework and quiz.

Answers for the lesson and practice sheets.

A double bar graph is used for displaying categorial data. If the data are grouped into categories, such as makes of automobiles, school subjects, or types of movies, it is called categorial data. Double bar graphs are used for comparisons between 2 groups.

Interpreting Histograms Worksheet Download

A histogram can be defined as a set of rectangles with bases along with the intervals between class boundaries. Each rectangle bar depicts some sort of data and all the rectangles are adjacent. The heights of rectangles are proportional to corresponding frequencies of similar as well as for different classes. Let's learn about histograms more in detail.

What is Histogram?

• A histogram is the graphical representation of data where data is grouped into continuous number ranges and each range corresponds to a vertical bar.
• The horizontal axis displays the number range.
• The vertical axis (frequency) represents the amount of data that is present in each range.

The number ranges depend upon the data that is being used.

Histogram Graph

A histogram graph is a bar graph representation of data. It is a representation of a range of outcomes into columns formation along the x-axis. in the same histogram, the number count or multiple occurrences in the data for each column is represented by the y-axis. It is the easiest manner that can be used to visualize data distributions. Let us understand the histogram graph by plotting one for the given below example.

Uncle Bruno owns a garden with 30 black cherry trees. Each tree is of a different height. The height of the trees (in inches): 61, 63, 64, 66, 68, 69, 71, 71.5, 72, 72.5, 73, 73.5, 74, 74.5, 76, 76.2, 76.5, 77, 77.5, 78, 78.5, 79, 79.2, 80, 81, 82, 83, 84, 85, 87. We can group the data as follows in a frequency distribution table by setting a range:

This data can be now shown using a histogram. We need to make sure that while plotting a histogram, there shouldn’t be any gaps between the bars.

How to Make a Histogram?

The process of making a histogram using the given data is described below:

• Step 1: Choose a suitable scale to represent weights on the horizontal axis.
• Step 2: Choose a suitable scale to represent the frequencies on the vertical axis.
• Step 3: Then draw the bars corresponding to each of the given weights using their frequencies.

Example: Construct a histogram for the following frequency distribution table that describes the frequencies of weights of 25 students in a class.

Steps to draw a histogram:

• Step 1: On the horizontal axis, we can choose the scale to be 1 unit = 11 lb. Since the weights in the table start from 65, not from 0, we give a break/kink on the X-axis.
• Step 2: On the vertical axis, the frequencies are varying from 4 to 10. Thus, we choose the scale to be 1 unit = 2.

Frequency Histogram

A frequency histogram is a histogram that shows the frequencies (the number of occurrences) of the given data items. For example, in a hospital, there are 20 newborn babies whose ages in increasing order are as follows: 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 5. This information can be shown in a frequency distribution table as follows:

This data can be now shown using a frequency histogram.

Histogram Shapes

The histogram can be classified into different types based on the frequency distribution of the data. There are different types of distributions, such as normal distribution, skewed distribution, bimodal distribution, multimodal distribution, comb distribution, edge peak distribution, dog food distribution, heart cut distribution, and so on. The histogram can be used to represent these different types of distributions. We have mainly 5 types of histogram shapes. They are listed below:

• Bell Shaped Histogram

Bimodal Histogram

Skewed right histogram, skewed left histogram, uniform histogram.

Let us discuss the above-mentioned types of histogram or histogram shapes in detail with the help of practical illustrations.

Bell-Shaped Histogram

A bell-shaped histogram has a single peak. The histogram has just one peak at this time interval and hence it is a bell-shaped histogram . For example , the following histogram shows the number of children visiting a park at different time intervals. This histogram has only one peak. The maximum number of children who visit the park is between 5.30 PM to 6 PM.

A bimodal histogram has two peaks and it looks like the graph given below. For example, the following histogram shows the marks obtained by the 48 students of Class 8 of St.Mary’s School. The maximum number of students have scored either between 40 to 50 marks OR between 60 to 70 marks. This histogram has two peaks (between 40 to 50 and between 60 to 70) and hence it is a bimodal histogram .

A skewed right histogram is a histogram that is skewed to the right. In this histogram, the bars of the histogram are skewed to the right, hence called a skewed right histogram . For example, the following histogram shows the number of people corresponding to different wage ranges. The histogram is skewed to the right. For the maximum number of people, wages ranged from 10-20(thousands)

A skewed left histogram is a histogram that is skewed to the left. In this histogram, the bars of the histogram are skewed to the left side, hence, called a skewed left histogram. For example, the following histogram shows the number of students of Class 10 of Greenwood High School according to the amount of time they spent on their studies on a daily basis. The maximum number of students study 4.5-5(hours) on daily basis.

A uniform histogram is a histogram where all the bars are more or less of the same height. In this histogram, the lengths of all the bars are more or less the same. Hence, it is a uniform histogram. For example, Ma’am Lucy, the Principal of Little Lilly Playschool, wanted to record the heights of her students. The following histogram shows the number of students and their varying heights. The height of the students ranges between 30 inches to 50 inches.

Difference Between a Bar Chart and a Histogram

The fundamental difference between histograms and bar graphs from a visual aspect is that bars in a bar graph are not adjacent to each other.

• A bar graph is the graphical representation of categorical data using rectangular bars where the length of each bar is proportional to the value they represent.

The main differences between a bar chart and a histogram are as follows:

But in both graphs, Y-axis represents numbers only. We can understand these differences from the following figure:

Histogram Calculator

A histogram calculator is a free online tool that graphs the histogram for a given data. In this calculator, you can enter the intervals and frequency given in the data and the histogram for that data will be displayed within a few seconds. Here is the Cuemath histogram calculator where you can enter a list of values of data and it will generate the corresponding histogram. Try now.

Tips and Tricks on Histogram

Following are the few important tips and tricks mentioned that to be kept in mind while visualizing any data via histogram.

• Choose the scale on the vertical axis while drawing a histogram, check for the highest number that divides all the frequencies. If there is no such number exists, then check for the highest number that divides most of the frequencies.
• A histogram is a graph that is used to summarise continuous data.
• A histogram gives the visual interpretation of continuous data.
• The scales of both horizontal and vertical axes don’t need to start from 0.
• There should be no gaps between the bars of a histogram.

Histogram Examples

Example 1: Consider the following histogram that represents the weights of 34 newborn babies in a hospital. If the children weighing between 6.5 lb to 8.5 lb are considered healthy, then find the percentage of the children of this hospital that are healthy.

We have to first find the number of children weighing between 4.4 lb to 6.6 lb. From the given histogram, the number of children weighing between:

6.5 lb - 7.5 lb = 10

7.5 lb - 8.5 lb = 18

Therefore, the number of children weighing between 6.5 lb to 8.5 lb = (10+18=28). The total number of children in the hospital = 34. Hence, the required percentage is: 28/34 × 100 = approx. 83%. ∴ Required percentage = 83%.

Example 2: A random survey is done on the number of children belonging to different age groups who play in government parks and the information is tabulated in the table given below.

(i) Draw a histogram representing the data.

(ii) Identify the number of children belonging to the age groups 2, 3, 4, 5, 6, and 7 who play in government parks.

(i) We take the age (in years) on the horizontal axis of the graph and by observing the first column of the table, we choose the scale to be: 1 unit = 1 year. We take frequency on the vertical axis of the graph and by observing the second column of the table, we choose the scale to be: 1 unit = 2. Now, we will draw the corresponding histogram.

(ii) From the table/graph, the number of children belonging to the age groups:

2 to 4 years = 10

4 to 7 years = 18

So, the number of children belonging to the age groups 2, 3, 4,5,6, and 7 who play in government parks is 10+18= 28. ∴ Required number of children = 28.

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Practice Questions on Histograms

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FAQs on Histogram

What is a histogram in statistics.

A histogram in statistics is a solid figure or diagram that consists of rectangular bars. It is one of the major forms of a bar graph that is used to visualize any given numeric data with a practical approach.

What is a Histogram Used For?

A histogram is used for showing the frequencies of different data. It is the graphical representation of data where the data is grouped into continuous number ranges and each range corresponds to a vertical bar.

☛ Read the basics about histograms here:

What is a Histogram Graph?

A histogram is a type of graph for the graphical representation of data. This data is grouped into number ranges and each range corresponds to a vertical bar.

☛ Also Check:

• Pictographs
• Line Graphs

How do you Construct a Histogram?

The steps to construct a histogram are as follows:

• Step 1: We place the intervals on the horizontal axis by choosing a suitable scale.
• Step 2: We place frequencies on the vertical axis by choosing a suitable scale.
• Step 3: We construct vertical bars according to the given frequencies.

What is the Difference Between a Bar Graph and a Histogram?

The fundamental difference between histograms and bar graphs from a visual aspect is that bars in a bar graph are not adjacent to each other. A bar graph has equal space between every two consecutive bars and X-axis can represent anything. On the other hand, a histogram has no space between two consecutive bars. They should be attached to each other and the X-axis should represent only continuous data that is in terms of numbers.

What is a Relative Frequency Histogram?

A relative frequency histogram is a kind of graphical representation only, that uses the same information as a frequency histogram. These compare each class interval to the total number of items.

☛ Read more about:

• Relative Frequency
• Relative Frequency Formula

How are Histograms Used Around?

A histogram is a type of bar chart only that is used to display the variation in continuous data, such as time, weight, size, or temperature. A histogram helps to recognize and analyze patterns in data that are not apparent simply by looking at a table of data, or by finding the average or median.

☛ Learn more about the below terminologies:

How Does a Histogram Represent Data?

A histogram is a graphical display of data with bars of different heights, where each bar groups numbers into ranges. The taller the bars, the more the data falls in that range. It displays the shape as well as the spread of continuous sample data.

Why Do We Use Kink in Histograms?

Kink is used to denote or represent a break on the axis of the histogram. There are some cases where data has huge figures or numeric values to represent such data via histogram we use the zigzag symbol known as kink. This kink helps in visualizing a given data by breaking it.

Why is a Histogram Two-Dimensional?

A histogram is a visual representation of data, a two-dimension graph that uses a set of vertical rectangles(emphasizing both the lengths and widths of the rectangles) to represent class frequencies of the given distribution. Click to learn more about frequency distribution here.

How do you Interpret the Skewness of a Histogram?

We can interpret the skewness of a histogram by looking into the following aspects.

• Normal distribution will have a skewness of 0.
• If the tail on the right side of the distribution will be longer, the skewness will be positive.
• If the tail on the left side of the distribution will be longer, the skewness will be negative.

• Math Article

In statistics, a histogram is a graphical representation of the distribution of data. The histogram is represented by a set of rectangles, adjacent to each other, where each bar represent a kind of data. Statistics is a stream of mathematics that is applied in various fields. When numerals are repeated in statistical data, this repetition is known as Frequency and which can be written in the form of a table, called a frequency distribution. A  Frequency distribution  can be shown graphically by using different types of graphs and a Histogram is one among them.  In this article, let us discuss in detail about what is a histogram , how to create the histogram for the given data, different types of the histogram, and the difference between the histogram and bar graph in detail.

What is Histogram?

A histogram is a graphical representation of a grouped frequency distribution with continuous classes. It is an area diagram and can b e defined as a set of rectangles with bases along with the intervals between class boundaries and with areas proportional to frequencies in the corresponding classes. In such representations, all the rectangles are adjacent since the base covers the intervals between class boundaries. The heights of rectangles are proportional to corresponding frequencies of similar classes and for different classes, the heights will be proportional to corresponding frequency densities.

In other words, a histogram is a diagram involving rectangles whose area is proportional to the frequency of a variable and width is equal to the class interval.

How to Plot Histogram?

You need to follow the below steps to construct a histogram.

• Begin by marking the class intervals on the X-axis and frequencies on the Y-axis.
• The scales for both the axes have to be the same.
• Class intervals need to be exclusive.
• Draw rectangles with bases as class intervals and corresponding frequencies as heights.
• A rectangle is built on each class interval since the class limits are marked on the horizontal axis, and the frequencies are indicated on the vertical axis.
• The height of each rectangle is proportional to the corresponding class frequency if the intervals are equal.
• The area of every individual rectangle is proportional to the corresponding class frequency if the intervals are unequal.

Although histograms seem similar to graphs, there is a slight difference between them. The histogram does not involve any gaps between the two successive bars.

When to Use Histogram?

The histogram graph is used under certain conditions. They are:

• The data should be numerical.
• A histogram is used to check the shape of the data distribution. 
• Used to check whether the process changes from one period to another.
• Used to determine whether the output is different when it involves two or more processes.
• Used to analyse whether the given process meets the customer requirements.

Difference Between Bar Graph and Histogram

A histogram is one of the most commonly used graphs to show the frequency distribution. As we know that the frequency distribution defines how often each different value occurs in the data set. The histogram looks more similar to the bar graph, but there is a difference between them. The list of differences between the bar graph and the histogram is given below:

The above differences can be observed from the below figures:

Bar Graph (Gaps between bars)

Histogram (No gaps between bars)

Types of Histogram

The histogram can be classified into different types based on the frequency distribution of the data. There are different types of distributions, such as normal distribution, skewed distribution, bimodal distribution, multimodal distribution, comb distribution, edge peak distribution, dog food distribution, heart cut distribution, and so on. The histogram can be used to represent these different types of distributions. The different types of a histogram are:

• Uniform histogram
• Symmetric histogram
• Bimodal histogram
• Probability histogram 

Uniform Histogram

A uniform distribution reveals that the number of classes is too small, and each class has the same number of elements. It may involve distribution that has several peaks.

Bimodal Histogram

If a histogram has two peaks, it is said to be bimodal. Bimodality occurs when the data set has observations on two different kinds of individuals or combined groups if the centers of the two separate histograms are far enough to the variability in both the data sets.

Symmetric Histogram

A symmetric histogram is also called a bell-shaped histogram. When you draw the vertical line down the center of the histogram, and the two sides are identical in size and shape, the histogram is said to be symmetric. The diagram is perfectly symmetric if the right half portion of the image is similar to the left half. The histograms that are not symmetric are known as skewed.

Probability Histogram

A Probability Histogram shows a pictorial representation of a discrete probability distribution. It consists of a rectangle centered on every value of x, and the area of each rectangle is proportional to the probability of the corresponding value. The probability histogram diagram is begun by selecting the classes. The probabilities of each outcome are the heights of the bars of the histogram.

Applications of Histogram

The applications of histograms can be seen when we learn about different distributions.

Normal Distribution

The usual pattern that is in the shape of a bell curve is termed normal distribution. In a normal distribution, the data points are most likely to appear on a side of the average as on the other. It is to be noted that other distributions appear the same as the normal distribution. The calculations in statistics are utilised to prove a distribution that is normal. It is required to make a note that the term “normal” explains the specific distribution for a process. For instance, in various processes, they possess a limit that is natural on a side and will create distributions that are skewed. This is normal which means for the processes, in the case where the distribution isn’t considered normal.

Skewed Distribution

The distribution that is skewed is asymmetrical as a limit which is natural resists end results on one side. The peak of the distribution is the off-center in the direction of the limit and a tail that extends far from it. For instance, a distribution consisting of analyses of a product that is unadulterated would be skewed as the product cannot cross more than 100 per cent purity. Other instances of natural limits are holes that cannot be lesser than the diameter of the drill or the call-receiving times that cannot be lesser than zero. The above distributions are termed right-skewed or left-skewed based on the direction of the tail.

Multimodal Distribution

The alternate name for the multimodal distribution is the plateau distribution. Various processes with normal distribution are put together. Since there are many peaks adjacent together, the tip of the distribution is in the shape of a plateau.

Edge peak Distribution

This distribution resembles the normal distribution except that it possesses a bigger peak at one tail. Generally, it is due to the wrong construction of the histogram, with data combined together into a collection named “greater than”.

Comb Distribution

In this distribution, there exist bars that are tall and short alternatively. It mostly results from the data that is rounded off and/or an incorrectly drawn histogram. For instance, the temperature that is rounded off to the nearest 0.2 o would display a shape that is in the form of a comb provided the width of the bar for the histogram were 0.1 o .

Truncated or Heart-Cut Distribution

The above distribution resembles a normal distribution with the tails being cut off. The producer might be manufacturing a normal distribution of product and then depending on the inspection to segregate what lies within the limits of specification and what is out. The resulting parcel to the end-user from within the specifications is heart cut.

Dog Food Distribution

This distribution is missing something. It results close by the average. If an end-user gets this distribution, someone else is receiving a heart cut distribution and the end-user who is left gets dog food, the odds and ends which are left behind after the meal of the master. Even if the end-user receives within the limits of specifications, the item is categorised into 2 clusters namely – one close to the upper specification and another close to the lesser specification limit. This difference causes problems in the end-users process.

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• Graphical Representation 

Histogram Solved Example

Question: The following table gives the lifetime of 400 neon lamps. Draw the histogram for the below data.

The histogram for the given data is:

Video Lesson

Frequently Asked Questions on Histogram

Are histogram and bar chart the same.

No, histograms and bar charts are different. In the bar chart, each column represents the group which is defined by a categorical variable, whereas in the histogram each column is defined by the continuous and quantitative variable.

Which histogram represents the consistent data?

The uniform shaped histogram shows consistent data. In the uniform histogram, the frequency of each class is similar to one other. In most cases, the data values in the uniform shaped histogram may be multimodal.

Can a histogram be drawn for the normally distributed data?

Yes, the histogram can be drawn for the normal distribution of the data. A normal distribution should be perfectly symmetrical around its center. It means that the right should be the mirror image of the left side about its center and vice versa.

When a histogram is skewed to right?

A histogram is skewed to the right, if most of the data values are on the left side of the histogram and a histogram tail is skewed to right. When the data are skewed to the right, the mean value is larger than the median of the data set.

When a histogram is skewed to the left?

A histogram is skewed to the left, if most of the data values fall on the right side of the histogram and a histogram tail is skewed to left. In this case, the mean value is smaller than the median of the data set.

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