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.