About Histogram in Math
What is a Histogram?
Definition: A histogram is a graphical representation of a group of data points organized into user-defined ranges. The histogram, which resembles a bar graph in appearance, condenses a data series into an easily interpreted visual by grouping data points into logical ranges or bins.
An example of a histogram is shown below:
Here the x-axis represents the time slots for a task, and the y-axis represents the frequency of work done in particular time slots. The frequency of the values in the interval is represented by the height of a bar on the graph.
Construction of a Histogram
There are some basic steps to construct a histogram of a specific data series.
Step 1: Draw and label the coordinate axes.
Step 2: Draw the bar by taking the help of the data in the given data series.
Comparison of Histogram
Difference between Histogram and Bar Graph
One of the most common graphs for displaying frequency distribution in statistics is the histogram. The frequency distribution, as we all know, determines how frequently each different value appears in the data set. The histogram resembles the bar graph in appearance, but there is a clear distinction between the two types of graphs. The following is a list of the differences between the bar graph and the histogram:
Solved Histogram Examples
Example 1: The winning speeds of car at the sports stadium are shown in the histogram.
a. How many of the winning cars have a top speed of at least 160 mph?
b. Which of the following intervals has the greatest number of data values?
c. What percentage of the winning speeds are under 140 mph?
Answer:
a. Eight winning speeds are in the 160 – 169 miles per hour interval, and five winning speeds are in the 170 – 179 miles per hour interval. So, 8 + 5 = 13 winning speeds are at least 160 miles per hour.
b. The interval with the tallest bar contains the most data values. So, the 150 – 159 miles per hour interval contains the most data values.
c. One winning speed is 120 – 129 in the miles per hour interval, and eight winning speeds are in the 130 – 139 miles per hour interval. So, 1 + 8 = 9 winning speeds are less than 140 miles per hour.
Example 2: The histogram depicts the number of magazines read by the students of a class in the previous year.
a. What is the total number of students in the class?
b. Which interval has the smallest number of data values?
c. What percentage of the students read less than six magazines per year?
Answer:
a. The number of students in the class are 15 + 3 + 2 = 20. Hence the total number of students is 20.
b. As we can see in the above histogram 4-5 interval shows no data and from there we can come to the conclusion that interval 4-5 has the smallest number of data values.
c. Total number of students who read less than 6 magazines is 15 + 2 = 17. So, percentage of students read less than six magazines per year = \(\frac{17}{20}\times 100\) = 85 %
One of the most popular graphing tools is known as the histogram and it’s used to summarize data that’s either discrete or continuous and measured on an interval scale. It is frequently used to visualize the major features of the data distribution in a convenient format.
A bar graph is a graphical representation of categorical data made up of rectangular bars whose length is proportional to the value represented. A histogram is a graphical representation of data in which the data is divided into continuous number ranges, each of which is represented by a vertical bar.
Histograms are primarily used to present and organise a vast number of measurements or numerical data in a user-friendly manner. A histogram will show you where the majority of numbers on a measuring scale fall, as well as how much variation there is among them.