Histogram

1. Histogram Prepared By; Anjana Shanti Priya (13MMF0022)

2. 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

3. Mathematical Definition In a more general mathematical sense, a histogram is a function  m i  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  m i  meets the following conditions:

4. When Are Histograms Used? Summarize large data sets graphically Compare measurements to specifications Communicate information to the team Assist in decision making

5. 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.

6. 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

7. 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

8. 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 :

9. Simple Example-2 Consider 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

10. Thank You