HistogramPrepared By;

Anjana Shanti Priya

(13MMF0022)

What Is Histogram?

It is a representation of a frequency distribution by means of rectangles whose widths represent class intervals and whose areas are proportional to the corresponding frequencies.

It Looks like

Mathematical DefinitionIn a more general mathematical sense, a histogram is a

function mi that counts the number of observations that fall into each of the disjoint categories (known as bins).

let n be the total number of observations and k be the total number of bins, the histogram mi meets the following conditions:

When Are Histograms Used?Summarize large data sets graphicallyCompare measurements to specificationsCommunicate information to the teamAssist in decision making

What are the parts of a Histogram?

Histogram is made up of five parts:

Title:

The title briefly describes the information that is contained in the Histogram.

Horizontal or X-Axis:

The horizontal or X-axis shows you the scale of values into which the measurements fit.

Bars:

The bars have two important characteristics—height and width. The height represents the number of times the values within an interval occurred. The width represents the length of the interval covered by the bar. It is the same for all bars.

Continue.

Vertical or Y-Axis:

The vertical or Y-axis is the scale that shows you the number of times the values within an interval occurred. The number of times is also referred to as "frequency.“

Legend:

The legend provides additional information that documents where the data came from and how the measurements were gathered

Steps of Histogram

Step 1 - Count number of data points

Step 2 - Summarize on a tally sheet

Step 3 - Compute the range

Step 4 - Determine number of intervals

Step 5 - Compute interval width

Step 6 - Determine interval starting points

Step 7 - Count number of points in each interval

Step 8 - Plot the data

Step 9 - Add title and legend

Simple Example-1 Consider the following set for example

{1,2,2,3,3,3,3,4,4,5,6} we can graph them like this:

Simple Example-2Consider the set {3, 11, 12, 19, 22, 23, 24, 25, 27, 29, 35, 36,

37, 45, 49}Instead of bin the data are converted into convenient ranges. In this case, with a bin width of 10, we can easily group the

data as below & we can construct histogram as below

Data Range Frequency

0-10 1

10-20 3

20-30 6

30-40 4

40-50 2

Thank You