From | To | Frequency | Density |
0 | 9 | 2 | 0.2 |
10 | 19 | 3 | 0.3 |
20 | 29 | 5 | 0.5 |
30 | 39 | 8 | 0.8 |
40 | 49 | 6 | 0.6 |
50 | 59 | 1 | 0.1 |
60 | 69 | 3 | 0.3 |
Here all ranges have the same length 10, and the histogram corresponding to these data would look like:
0.8 ##### 0.7 ##### 0.6 ########## 0.5 ############### 0.4 ############### 0.3 #################### ##### 0.2 ######################### ##### 0.1 ###################################0---10---20---30---40---50---60---70
Suppose we group the above data differently:
From | To | Frequency | Density |
0 | 9 | 2 | 0.2 |
10 | 19 | 3 | 0.3 |
20 | 59 | 20 | 0.5 |
60 | 69 | 3 | 0.3 |
0.8 0.7 0.6 0.5 #################### 0.4 #################### 0.3 ############################## 0.2 ################################### 0.1 ###################################0---10---20---30---40---50---60---70
The distinction between a histogram and a bar graph is that if we wish to find the total frequency of a range of values, we must consider the area under the graph in that range. For instance, for the histogram above, the area under the graph in the range 0-20 is 10×0.2 + 10× 0.3 for a total frequency of 5.
If a histogram is based on relative frequencies (i.e. percentages) as opposed to absolute frequencies as above, then it will resemble the underlying random variable's probability density function and the area under the histogram will always be 1.