# Box and Whisker Chart

Let's say 7 students get the following scores in 2 subjects:

Student |
Ann | Jacob | Susan | Rose | Tom | Peter | Kate |

Maths |
35 | 78 | 91 | 42 | 56 | 66 | 71 |

Physics |
85 | 68 | 70 | 30 | 78 | 83 | 45 |

You have to visualize the distribution of their scores. The Box and Whisker chart can come in handy in such scenarios!

The Box & Whisker chart displays the spread and skewness in a batch of data through its five-number summary: minimum, maximum, median, upper and lower quartiles. It is used:

- For a quick understanding of the distribution of a dataset
- To know whether a distribution is skewed or not
- To find out unusual observations/errors in the data set

Box and whisker plots are also very useful when large numbers of observations are involved and when two or more data sets are being compared.

The Box and Whisker consists of two parts—the main body called the Box and the thin vertical lines coming out of the Box called Whiskers .

### Constructing a Box and Whisker chart:

To understand how a Box and Whisker chart is constructed, we have to first arrange our data in ascending order.

The ordered data sets are :

Scores in Maths: 35, 42, 56, 66, 71, 78, 91

Scores in Physics: 30, 45, 68, 70, 78, 83, 85

Now let us find the median, the first (lower) quartile and the third (upper) quartile

The **median** is the point at which there are an equal number of data points whose values lie above and below the median value. [It is considered to be a better measurement of central tendency (most probable occurrence) in case of skewed distribution.]

In the example above,

Scores in Maths: 35, 42, 56, **66**, 71, 78, 91

Scores in Physics: 30, 45, 68, **70**, 78, 83, 85

66 and 70 are the median values in Maths and Physics respectively (there are 3 data points both above and below these values).

The **First (Lower) Quartile** is the midpoint of the lower half of our data.

Lower half of scores in Maths (in Bold): **35**,** 42**,** 56,** 66, 71, 78, 91

Lower half of scores in Physics (in Bold): **30**,** 45**,** 68**, 70, 78, 83, 85

42 and 45 are the first quartiles in Maths and Physics respectively (there is 1 data point both above and below)

**The Third (Upper) Quartile** is the midpoint of the upper half of our data.

Upper half of scores in Maths (in Bold): 35, 42, 56, 66, **71**,** 78**,** 91**

Upper half of scores in Physics (in Bold): 30, 45, 68, 70, **78**,** 83**,** 85**

78 and 83 are the third quartiles in Maths and Physics respectively (there is 1 data point both above and below).

A quick summary of the values for our Box and Whisker chart:

Maths | Physics |
---|---|

Median= 66 | Median= 70 |

Lower quartile= 42 | Lower quartile= 45 |

Upper quartile= 78 | Upper quartile= 83 |

Minimum value= 35 | Minimum value= 30 |

Maximum value= 91 | Maximum value= 85 |

Now letâ€™s see how these values translate into our Box and Whisker chart:

The first quartile forms the bottom and the third quartile forms the top of the Box. The Whiskers connect the minimum and the maximum values to the Box.

In addition to showing median, first and third quartile and maximum and minimum values, the Box and Whisker chart is also used to depict Mean, Standard Deviation, Mean Deviation and Quartile Deviation.

**Depicting Mean in Box and Whisker chart: Analysis of Flight Departure Delays**

Let us assume there were 5 Flights leaving an airport and data was collected for a period of 5 days.

DEPARTURE DELAYS (in mins)

Mon | Tue | Wed | Thu | Fri | |
---|---|---|---|---|---|

Flight 1 | 5 min | 1 min | 10 min | 1 min | 6 min |

Flight 2 | 0 min | 6 min | 2 min | 10 min | 5 min |

Flight 3 | 1 min | 3 min | 5 min | 2 min | 2 min |

Flight 4 | 9 min | 10 min | 3 min | 2 min | 1 min |

Flight 5 | 1 min | 2 min | 3 min | 6 min | 4 min |

The resulting Box and Whisker chart from this data looks like:

Note that in addition to details like median, quartiles, maximum and minimum values, the chart also shows the mean(average) values (triangular icon),giving an idea of the average delay per day in flight departures.

Box and Whisker charts find their application in Statistical Analysis, Scientific Analysis, Test Results Analysis, Marketing Analysis, Networking Data Analysis, Analytics and General Analysis

Check out some more examples of the Box and Whisker chart here.

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