7.2. Bar Graphs, Histograms and Stem-and-Leaf Plots http://www.ck12.org
Histograms
Ahistogramis very similar to a bar graph with no spaces between the bars. The bars are all along side each other.
The groups of data or bins are plotted on thex−axisand their frequencies are on they−axis. In most cases, the
bins are designed so that there is no break in the groups. This means that if you had a set of data grouped in bin sizes
of ten and the data ranged from zero to fifty, the bins would be represented as[ 0 − 10 );[ 10 − 20 );[ 20 − 30 );[ 30 −
40 );[ 40 − 50 )and[ 50 − 60 ). If you count the number of numbers in each bin, you see that it is 11. You are supposed
to have a bin size of 10. The notation [,) means that the first number in each bin is after the square bracket [but the last
number) actually counts in the next group. Although the bins are written in this manner, the bin really extends 0 to
9, 10 to 19 etc. when the data is grouped. Histograms are usually drawn with the data from a frequency distribution
table –often called a frequency table. Like a bar graph, a histogram requires a title and properly labeledxandyaxes.
Example 1:Studies (and logic) show that the more homework you do the better your grade in a course. In a study
conducted at a local school, students in grade 10 were asked to check off what box represented the average amount
of time they spent on homework each night. The following results were recorded:
TABLE7.6:
Time Spent on Homework
(Hours)Tally Frequency (# of students)[ 0 − 0. 5 ) @||||@@||||||@ 12
[ 0. 5 − 1. 0 ) @||||@@||||@@||||@@|||||||@ 23
[ 1. 0 − 1. 5 ) @||||@@||||@@||||@@||||@@||||@@||||||||@ 34
[ 1. 5 − 2. 0 ) @||||@@||||@@||||@@||||@@|||||@ 26
[ 2. 0 − 2. 5 ) @||||@ 5
2. 5 + 0This data will now be represented by drawing a histogram.
As with the bar graph, the actual data values are not plotted because the data has been grouped in bins.
An extension of the histogram is a frequency polygon graph. Afrequency polygonsimply joins the midpoints
(the center of the tops of the bars) of the histogram class intervals with straight lines and then extends these to the
horizontal axis. The distribution is extended one unit before the smallest recorded data and one unit beyond the
largest recorded data. Looking at the histogram below, we can draw the frequency polygon on top of the histogram.
The area under the frequency polygon is the same as the area under the histogram and is therefore equal to the
frequency values in the table. The frequency polygon also the shape of the distribution of the data and in this case it
resembles the bell curve.