## How to make a box and whisker plot

Read,3 minutes

### What Is A Box and Whisker Plot?

These are graphical **depictions **of variation in a data set. Normally, a **histogram** analysis would suffice, however, a box and plot will provide better **detail** whilst additionally letting **several** data sets be shown via the **same** graph.

**Median**(\(Q_{2}\) / \(50\)th percentile):**Middle**value of the data set**First**Quartile (\(Q_{1}\)): \(25\)th percentile of the data set**Third**Quartile (\(Q_{3}\)): \(75\)th percentile of the data set

### 5 Number Summary

The way to create a box and plot comes from the 5 following statistics:

**Minimum value:**The**smallest**data set value.**2nd quartile:**Value**under**which the**lower**\(25\) percent of the data are confined.**Median value: Middle**number in a group of numbers.**3rd quartile:**Value**over**which the**top**\(25\) percent of the data are confined.**Maximum value: Biggest**data set value.

Now that you understand the 5-number summary as well as the **vital** points, we can look at some steps for **creating** a box and whiskers plot.

### How do you Make a Box and Whisker Plot?

**Step one:**Arrange the data from**least**to**most.****Step two:**Determine the**median.****Step three:**Determine the**quartiles.****Step four:**Complete the**5-number**summary via calculating the**minimum**as well as the**maximum**values.

### Creating a Box Plot

**Step one:**Scale as well as**label**an**axis**which matches the 5-number summary.**Step two:**Draw whiskers going from \(Q_{1}\) to the**min-age**value as well as going \(Q_{3}\) to the**max-age**value.

The graph you end up with provides the **minimum, median,** lower and upper **quartile,** as well as the **max-age** value of the pupils contained in the dataset.

### Exercises for Box and Whisker Plots

**1) **Write the five-number summary for the set of data: \(41, \ 27, \ 30, \ 64, \ 47, \ 52, \ 47, \ 27, \ 63\)

**2) **Write the five-number summary for the set of data: \(37, \ 72, \ 33, \ 61, \ 39, \ 52, \ 80, \ 60\)

**3) **Write the five-number summary for the set of data: \(15, \ 32, \ 17, \ 28, \ 12, \ 28, \ 35, \ 17, \ 24\)

**4) **Write the five-number summary for the set of data: \(57, \ 69, \ 54, \ 81, \ 65, \ 52, \ 57, \ 61\)

**5) **Write the five-number summary for the set of data: \(72, \ 68, \ 75, \ 70, \ 65, \ 61, \ 82, \ 81\)

**6) **Write the five-number summary for the set of data: \(29, \ 35, \ 18, \ 53, \ 12, \ 32, \ 17, \ 25, \ 41\)

**7) **Write the five-number summary for the set of data: \(73, \ 83, \ 67, \ 63, \ 59, \ 75, \ 55, \ 69, \ 59\)

**8) **Write the five-number summary for the set of data: \(75, \ 85, \ 98, \ 93, \ 61, \ 78, \ 65, \ 76, \ 68\)

**9) **Write the five-number summary for the set of data: \(99, \ 89, \ 108, \ 76, \ 105, \ 73, \ 93, \ 82\)

**10) **Write the five-number summary for the set of data: \(82, \ 66, \ 89, \ 95, \ 69, \ 98, \ 61, \ 78, \ 73, \ 80\)

**1) **Write the five-number summary for the set of data: \(41, \ 27, \ 30, \ 64, \ 47, \ 52, \ 47, \ 27, \ 63\)

First, we should arrange the given data from smallest to highest: \(\color{red}{27, \ 27, \ 30, \ 41, \ 47, \ 47, \ 52, \ 63, \ 64}\)

Now, according to the above data:

- \(\color{red}{Minimum \ = \ 27}\)
- \(\color{red}{Q_1 \ = \ \frac{27 \ + \ 30}{2} \ = \ 28.5}\)
- \(\color{red}{Q_2 \ = \ 47}\)
- \(\color{red}{Q_3 \ = \ \frac{52 \ + \ 63}{2} \ = \ 57.5}\)
- \(\color{red}{Maximum \ = \ 64}\)

**2) **Write the five-number summary for the set of data: \(37, \ 72, \ 33, \ 61, \ 39, \ 52, \ 80, \ 60\)

First, we should arrange the given data from smallest to highest: \(\color{red}{33, \ 37, \ 39, \ 52, \ 60, \ 61, \ 72, \ 80}\)

Now, according to the above data:

- \(\color{red}{Minimum \ = \ 33}\)
- \(\color{red}{Q_1 \ = \ 37}\)
- \(\color{red}{Q_2 \ = \ \frac{52 \ + \ 60}{2} \ = \ 56}\)
- \(\color{red}{Q_3 \ = \ 72}\)
- \(\color{red}{Maximum \ = \ 80}\)

**3) **Write the five-number summary for the set of data: \(15, \ 32, \ 17, \ 28, \ 12, \ 28, \ 35, \ 17, \ 24\)

First, we should arrange the given data from smallest to highest: \(\color{red}{12, \ 15, \ 17, \ 17, \ 24, \ 28, \ 28, \ 32, \ 35}\)

Now, according to the above data:

- \(\color{red}{Minimum \ = \ 12}\)
- \(\color{red}{Q_1 \ = \ \frac{15 \ + \ 17}{2} \ = \ 16}\)
- \(\color{red}{Q_2 \ = \ 24}\)
- \(\color{red}{Q_3 \ = \ \frac{28 \ + \ 32}{2} \ = \ 30}\)
- \(\color{red}{Maximum \ = \ 35}\)

**4) **Write the five-number summary for the set of data: \(57, \ 69, \ 54, \ 81, \ 65, \ 52, \ 57, \ 61\)

First, we should arrange the given data from smallest to highest: \(\color{red}{52, \ 54, \ 57, \ 57, \ 61, \ 65, \ 69, \ 81}\)

Now, according to the above data:

- \(\color{red}{Minimum \ = \ 52}\)
- \(\color{red}{Q_1 \ = \ 54}\)
- \(\color{red}{Q_2 \ = \ \frac{57 \ + \ 61}{2} \ = \ 59}\)
- \(\color{red}{Q_3 \ = \ 69}\)
- \(\color{red}{Maximum \ = \ 81}\)

**5) **Write the five-number summary for the set of data: \(72, \ 68, \ 75, \ 70, \ 65, \ 61, \ 82, \ 81\)

First, we should arrange the given data from smallest to highest: \(\color{red}{61, \ 65, \ 68, \ 70, \ 72, \ 75, \ 81, \ 82}\)

Now, according to the above data:

- \(\color{red}{Minimum \ = \ 61}\)
- \(\color{red}{Q_1 \ = \ 65}\)
- \(\color{red}{Q_2 \ = \ \frac{70 \ + \ 72}{2} \ = \ 71}\)
- \(\color{red}{Q_3 \ = \ 81}\)
- \(\color{red}{Maximum \ = \ 82}\)

**6) **Write the five-number summary for the set of data: \(29, \ 35, \ 18, \ 53, \ 12, \ 32, \ 17, \ 25, \ 41\)

First, we should arrange the given data from smallest to highest: \(\color{red}{12, \ 17, \ 18, \ 25, \ 29, \ 32, \ 35, \ 41, \ 53}\)

Now, according to the above data:

- \(\color{red}{Minimum \ = \ 12}\)
- \(\color{red}{Q_1 \ = \ \frac{17 \ + \ 18}{2} \ = \ 17.5}\)
- \(\color{red}{Q_2 \ = \ 29}\)
- \(\color{red}{Q_3 \ = \ \frac{35 \ + \ 41}{2} \ = \ 38}\)
- \(\color{red}{Maximum \ = \ 53}\)

**7) **Write the five-number summary for the set of data: \(73, \ 83, \ 67, \ 63, \ 59, \ 75, \ 55, \ 69, \ 59\)

First, we should arrange the given data from smallest to highest: \(\color{red}{55, \ 59, \ 59, \ 63, \ 67, \ 69, \ 73, \ 75, \ 83}\)

Now, according to the above data:

- \(\color{red}{Minimum \ = \ 55}\)
- \(\color{red}{Q_1 \ = \ \frac{59 \ + \ 59}{2} \ = \ 59}\)
- \(\color{red}{Q_2 \ = \ 67}\)
- \(\color{red}{Q_3 \ = \ \frac{73 \ + \ 75}{2} \ = \ 74}\)
- \(\color{red}{Maximum \ = \ 83}\)

**8) **Write the five-number summary for the set of data: \(75, \ 85, \ 98, \ 93, \ 61, \ 78, \ 65, \ 76, \ 68\)

First, we should arrange the given data from smallest to highest: \(\color{red}{61, \ 65, \ 68, \ 75, \ 76, \ 78, \ 85, \ 93, \ 98}\)

Now, according to the above data:

- \(\color{red}{Minimum \ = \ 61}\)
- \(\color{red}{Q_1 \ = \ \frac{65 \ + \ 68}{2} \ = \ 66.5}\)
- \(\color{red}{Q_2 \ = \ 76}\)
- \(\color{red}{Q_3 \ = \ \frac{85 \ + \ 93}{2} \ = \ 89}\)
- \(\color{red}{Maximum \ = \ 98}\)

**9) **Write the five-number summary for the set of data: \(99, \ 89, \ 108, \ 76, \ 105, \ 73, \ 93, \ 82\)

First, we should arrange the given data from smallest to highest: \(\color{red}{73, \ 76, \ 82, \ 89, \ 93, \ 99, \ 105, \ 108}\)

Now, according to the above data:

- \(\color{red}{Minimum \ = \ 73}\)
- \(\color{red}{Q_1 \ = \ 76}\)
- \(\color{red}{Q_2 \ = \ \frac{89 \ + \ 93}{2} \ = \ 91}\)
- \(\color{red}{Q_3 \ = \ 105}\)
- \(\color{red}{Maximum \ = \ 108}\)

**10) **Write the five-number summary for the set of data: \(82, \ 66, \ 89, \ 95, \ 69, \ 98, \ 61, \ 78, \ 73, \ 80\)

First, we should arrange the given data from smallest to highest: \(\color{red}{61, \ 66, \ 69, \ 73, \ 78, \ 80, \ 82, \ 89, \ 95, \ 98}\)

Now, according to the above data:

- \(\color{red}{Minimum \ = \ 61}\)
- \(\color{red}{Q_1 \ = \ 69}\)
- \(\color{red}{Q_2 \ = \ \frac{78 \ + \ 80}{2} \ = \ 79}\)
- \(\color{red}{Q_3 \ = \ 89}\)
- \(\color{red}{Maximum \ = \ 98}\)