Histogram represents data in the form of a diagram and it becomes easy
for the reader to analyse and interpret to come to various conclusions
and decisions. In histogram the figures are given the size
proportionally so that analysis can be done by non qualified and non
technical person too. |

**If 'd' is the gap between the upper limit of any class and the lower limit of the succeeding class the class boundaries for any class are then given by:**

Upper class boundary = Upper class limit + $\frac{d}{2}$

Lower class boundary = Lower class limit + $\frac{d}{2}$ Individual data points are grouped together in classes, so that you can get an idea of how frequently data in each class occur in the data set. A histogram with more number of class intervals is more effective in depicting the structure of the frequency distribution.

Different types of histograms are explained below.

**Frequency histogram**Histogram is a graphical display of data using bars of different heights.

The relative frequency table is a compact numerical way to present how the data is distributed. If the frequencies are plotted as columns, the resulting plot is called a histogram.

*Double peaked distribution*Looks like the back of a two humped camel. Outcomes of two processes with different distributions are combined in one set of data. In some cases bimodal histogram indicates that the sample can be divided into two sub samples that differ from each other in some way.It will have two peaks.

*J shaped distribution*Extreme case of negative skew. The reverse J or ‘ski-jump’ shape is an extreme case of positive skew. Cases are scoring tight up against a fixed end limit of a scale. J is like a heap which has one half missing, because the scale comes to an end so there is nowhere for the expected other half of the distribution to fall.

**Skewed Histogram**A non symmetric histogram is called skewed if it is not symmetric. If the upper tail is longer than the lower tail then it is positively skewed. If the upper tail is shorter than it is negatively skewed. A skewed distribution is one that is not symmetrical, but rather has a long tail in one direction.

*Uniform Histogram*A uniform distribution often means that the number of classes is too small, each class has about the same number of elements. It may describe a distribution which has several peaks. Uniform histogram have all the bars of same height.

**Example 1:**Distribution of marks of 250 students is obtained as follows.

Draw a histogram for the given data.

Marks |
Number of students |

14.5 - 19.5 | 9 |

19.5 - 24.5 | 11 |

24.5 - 29.5 | 10 |

29.5 - 34.5 | 44 |

34.5 - 39.5 | 45 |

39.5 - 44.5 | 54 |

44.5 - 49.5 | 37 |

49.5 - 54.5 | 26 |

54.5 - 59.5 | 8 |

59.5 -64.5 | 5 |

64.5 - 69.5 | 1 |

**Solution:**Since the grouped frequency distribution is not continuous, we first convert it into a continuous distribution with exclusive type classes as given below. The upper and lower class limits of the new exclusive type classes are known as class boundaries.

**Example 2:**Draw a histogram for the following data

Class Interval |
Frequency |

0 - 10 | 5 |

10 - 20 | 8 |

20 - 30 | 12 |

30 - 40 | 16 |

40 - 50 | 7 |

50 - 60 | 15 |

60 - 70 | 17 |

70 - 80 | 19 |

80 - 90 | 25 |

90 -100 | 28 |

**Solution:**