 ## How to make a box and whisker plot

### 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:

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

## Box and Whisker Plots Quiz

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