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Field and Whiskers Plot




A field and whiskers plot, additionally referred to as field plot, is a graph that summarizes of set of knowledge alongside a quantity line from least to biggest as a way to present how information gadgets are unfold out. Earlier than learning this lesson about field plot, you might want to grasp what the median is.

Mainly a field and whiskers plot seems just like the graph you see beneath. Similar to the identify suggests, a field plot has two principal parts, a field within the center and whiskers at both aspect.


Box and Whiskers Plot

Now the explanation we name the 2 strains extending from the sting of the field “whiskers” is just because they seem like whiskers or mustache, particularly mustache of a cat.

The 5 elements of a field and whiskers plot

The 5 factors or dot that you just see within the determine signify the 5 elements of a field and whiskers plot and these elements are minimal, decrease quartile, median, uppper quartile, and most.

  • The minimal, additionally referred to as the decrease excessive is the bottom worth or smallest worth in a set of knowledge.
  • The decrease quartile, additionally referred to as the primary quartile or Q1, is the median of all information beneath the median. The decrease quartile may be referred to as the median of the decrease half.
  • The median, additionally referred to as the second quartile or Q2 is the center worth of the set of knowledge. If there are two values within the center, the median is the typical of the 2 values. The median may be referred to as the center quartile.
  • The higher quartile, additionally referred to as the third quartile or Q3 is the median of all information above the median. The higher quartile may be referred to as the median of the higher half.
  • The most, additionally referred to as the higher excessive, is the best worth in a set of knowledge.

Definition of some helpful phrases 

Interquartile vary

The interquartile vary (IQR) is the distinction between the third quartile and the primary quartile. 

Interquartile vary = Q3 – Q1 

Decrease interior fence

The decrease interior fence is the purpose that’s 1.5 × IQR beneath the primary quartile or Q1.

Decrease outer fence

The decrease outer fence is the purpose that’s 3 × IQR beneath the primary quartile or Q1.

Higher interior fence

The higher interior fence is the purpose that’s 1.5 × IQR above the third quartile Q3.

Higher outer fence

The higher outer fence is the purpose that’s 3 × IQR above the third quartile or Q3.

Outliers or excessive values

Values which are both very huge or very small compared with nearly all of the values in a set of knowledge are referred to as outliers or excessive values. We use an asterisk to point out this on the field and whiskers plot. 

If a worth is exterior both of the 2 interior fences, however throughout the two outer fences, this worth is a gentle outlier.

If a worth is exterior both of the 2 outer fences, this worth is an excessive outlier.

make a field and whiskers plot 

Observe the 5 steps beneath to assemble or make a field and whisker plot

  1. Put the information in rising order after which calculate the median, the primary quartile, the third quartile, and the interquartile vary.
  2. Create the field with the primary quartile, the median, and the third quartile. Contained in the field, draw additionally a vertical line on the place of the median.
  3. Discover the decrease and the higher interior fences and if needed the decrease and the higher outer fences.
  4. Discover the smallest and largest values within the information set which are throughout the decrease and the higher interior fences.
  5. Use the smallest and largest values to attract the whiskers. Then, present any outliers or values that falls exterior the 2 interior fences with an asterisk. 

An instance exhibiting find out how to create a field and whiskers plot

Instance #1

Assemble a field and whiskers plot for the information set: {5, 2, 16, 9, 13, 7, 10}

Step 1

First, it’s a must to put the information set so as from least to biggest.

From least to biggest we get: 2    5    7    9    10     13    16

Rigorously trying on the set we see that 9 is situated proper in the midst of the set of knowledge.
Subsequently, 9 is the median.

Now to get the primary quartile, you want all information earlier than the median or 9.

2    5    7    9    10     13    16

In purple proper above we present all information earlier than 9, so  2    5    7   

Because the worth in the midst of the set 2    5    7 is 5, the first quartile or Q1 is 5.

To get the third quartile, you want all information after the median or 9.

2    5    7    9    10     13    16

In purple proper above we present all information after 9, so  10    13    16   

Because the worth in the midst of the set 10    13    16 is 13, the third quartile or Q3 is 13.

Discover the interquartile vary (IQR)

IQR = 13 – 5 = 8

Step 2

Create the field with with the primary quartile, the median, and the third quartile. Contained in the field, draw additionally a vertical line on the place of the median.

Box showing first quartile, median, and third quartile

Step 3

Discover the decrease and higher interior fences.

1.5 × IQR = 1.5 × 8 = 12

Decrease interior fence = 5 – 12 = -7

Higher interior fence = 13 + 12 = 25 

Step 4

Discover 2 is greater than -7 and 16 is smaller than 25. The smallest and largest values within the information set which are throughout the decrease and the higher interior fences are 2 and 16 respectively. Subsequently, the minimal is 2 and the utmost is 16.

Step 5

Use the smallest and largest values so as to add the whiskers. 

Unfinished box and whiskers plot showing first quartile, median, third quartile, minimum, and maximum.

Lastly, draw horizontal segments or whiskers that join all 5 dots collectively. Your graph ought to seem like this after you might be carried out. The field and whiskers plot for {5, 2, 16, 9, 13, 7, 10} is the graph beneath.

Box and whiskers plot for 5, 2, 16, 9, 13, 7, and 10

create a field and whiskers plot with outliers

Instance #2

Assemble a field and whiskers plot for the information set: {5, 26, 2, 1, 9, 13, 7, 10, 17, 8, 12}

Step 1

First, it’s a must to put the information set so as from least to biggest.

From least to biggest we get:

1   2    5    7    8         9        10    12    13     17     26

The median is 9, the primary quartile is 5, and the third quartile is 13. 

IQR = 13 – 5 = 8

Step 2

Create a field by placing the median, the primary quartile, and the third quartile on the quantity line identical to it was carried out earlier.

Box showing first quartile, median, and third quartile

Step 3

Discover the decrease and higher interior fences.

1.5 × IQR = 1.5 × 8 = 12

Decrease interior fence = 5 – 12 = -7

Higher interior fence = 13 + 12 = 25 

Step 4

Discover 1 is greater than -7 and 17 is smaller than 25. The smallest and largest values within the information set which are throughout the decrease and the higher interior fences are 1 and 17 respectively. Subsequently, the bottom quantity is 1 and highest quantity is 17.

Step 5

Use the smallest and largest values so as to add the whiskers. 

Box and Whiskers Plot

The higher interior fence is 25. Thus, 26 is an outlier since it’s greater than the higher interior fence. Lastly, draw horizontal segments or whiskers that join all 5 dots collectively. Present the outlier with an asterisk.

You may clearly see that 26 is much better than the opposite values of the information set. Your graph ought to seem like the one you see beneath after you might be carried out. 

Box and whiskers plot with an outlier








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