Creating a Box-and-Whisker Plot



Creating a Box-and-Whisker Plot

Let's look at the quality rating for natural peanut butter:

|71.00 |

|69.00 |

|60.00 |

|60.00 |

|57.00 |

|52.00 |

|34.00 |

|89.00 |

|69.00 |

|69.00 |

|67.00 |

|63.00 |

|57.00 |

|40.00 |

For the regular peanut butter:

|76.00 |

|60.00 |

|54.00 |

|43.00 |

|40.00 |

|35.00 |

|34.00 |

|33.00 |

|31.00 |

|23.00 |

|23.00 |

|11.00 |

|83.00 |

|83.00 |

|54.00 |

|49.00 |

|46.00 |

|45.00 |

|40.00 |

|34.00 |

|31.00 |

|29.00 |

|26.00 |

First we will create a five number summary of the data and then create a box-and-whisker graph using these values.

First we will look at the data for the natural brands:

Step 1: Arrange the data from smallest to largest and label them from 1 to the number of data points:

34.00 |40.00 |52.00 |57.00 |57.00 |60.00 |60.00 |63.00 |67.00 |69.00 |69.00 |69.00 |71.00 |89.00 | data | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | rank | |tip: If you have the data in a spreadsheet you can highlight the column holding the data and sort it in ascending order.

Step 2: Find the median of the data:

We have 14 data values, so to compute the median of an even number of data values we compute the mean of the two middle values: 7 and 8 (14/2 = 7, 14/2 + 1 = 8) . So with the data above we get : (60.00+63.00)/2 = 61.5

Step 3: Find the lower quartile:

Now we just consider the data values less than the median of 61.5:

34.00 |40.00 |52.00 |57.00 |57.00 |60.00 |60.00 | data | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | rank | |The lower quartile is the median of the numbers above. Since we have an odd number of data points the median is the data value with rank (7+1)/2 = 4. So the lower quartile is 57.00.

Step 4: Find the upper quartile:

Now just look at the data values above the median (we ranked them from 1 to 7 to compute the median of this group):

63.00 |67.00 |69.00 |69.00 |69.00 |71.00 |89.00 | data | |1 | 2 |3 | 4 | 5 | 6 | 7 | rank | |The upper quartile is the median of the numbers above. Since we have an odd number of data points the median is the data value with rank (7+1)/2 = 4. So the upper quartile is 69.00.

Step 4: Find the minimum and maximum value:

34.00 |40.00 |52.00 |57.00 |57.00 |60.00 |60.00 |63.00 |67.00 |69.00 |69.00 |69.00 |71.00 |89.00 | data | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | rank | |with the data ordered it is easy to see the minimum value is 34.00 and the maximum value 89.00.

Step 5: Create the Box-and-Whisker Plot:

We are now ready to create our Box-and-Whisker plot:

Quality ratings for natural peanut butter:

[pic]

The rectangle is drawn from the lower quartile (57.00) to the upper quartile (69.00) the vertical line in the middle is the median (61.5). The whiskers extend to the minimum value (34.00) and the maximum value (89.00).

Step 6 : Title Your Plot

We can compare the quality ratings of the regular brands to the quality ratings of the natural brands by computing a box-and-whisker graph for the quality ratings of the regular brands on top of the box-and-whisker graph of the quality ratings for the regular brands:

Quality Ratings of Peanut Butter

[pic]

It is very easy to see the differences in the medians and range of quality ratings for the natural and regular brands of peanut butter. If we had a third group such as organic brands, we could compare them by computing the box-n-whisker graph on top of our two existing graphs.

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