Question

1. # Draw The Box-And-Whisker Plot For The Data. 21 29 25 20 36 28 32 35 28 30 29 25 21 35 26 35 20 19

Box-and-whisker plots are one of the most popular graphical representations of data in statistics. It can help you quickly identify outliers and other patterns in data sets, as well as assess their shape and central tendency. In this blog post, we’ll walk through the steps for drawing a box-and-whisker plot for the data set: 21 29 25 20 36 28 32 35 28 30 29 25 21 35 26 35 20 19. We’ll also explain how to interpret the information contained in the graph. By the end of this article, you should be able to draw your own Box-and-Whisker Plots with ease!

## What is a box-and-whisker plot?

A box-and-whisker plot is a graphical tool used to display the distribution of data. It is composed of a box, which represents the middle 50% of the data, and whiskers that extend from the box to show the rest of the data. The length of the whiskers indicates how spread out the data is.

There are several ways to construct a box-and-whisker plot. The most common method is to use the five-number summary: minimum, first quartile, median, third quartile, and maximum. To find these values, order the data from smallest to largest and then find the median. The first and third quartiles are found by finding the medians of the data above and below the median, respectively. The minimum and maximum are simply the smallest and largest values in the data set.

Once you have these five values, you can plot them on a number line. The minimum and maximum are plotted as points, and the first and third quartiles are plotted as lines that extend from the point representing the median. Finally, whiskers are drawn from each end of the box to represent all other data points.

## How to draw a box-and-whisker plot

To draw a box-and-whisker plot, you need to calculate the median, first quartile, and third quartile of the data. The median is the middle value when the data is sorted in order from least to greatest. The first quartile is the median of the data that is less than the overall median. The third quartile is the median of the data that is greater than the overall median.

Once you have calculated these values, you can plot them on a graph. To do this, draw a horizontal line segment for each value. For the median, draw a line segment from the first quartile to the third quartile. For the first and third quartiles, draw a line segment from the bottom (first quartile) or top (third quartile) of the box to the corresponding value on the x-axis. Finally, draw vertical lines from each end of each horizontal line segment to connect them and create your box-and-whisker plot!

## What do the different parts of a box-and-whisker plot represent?

The different parts of a box-and-whisker plot represent the following:

-The bottom of the box represents the first quartile (Q1), which is the 25th percentile.
-The top of the box represents the third quartile (Q3), which is the 75th percentile.
-The line in the middle of the box represents the median, which is the 50th percentile.
-The whiskers represent the minimum and maximum values, which are also known as the extremes.

## How to interpret a box-and-whisker plot

The box-and-whisker plot is a graphical representation of data that shows the distribution of a data set. The plot is divided into four sections, each representing a quartile of the data. The whiskers represent the minimum and maximum values of the data, and the box represents the second and third quartiles.

To interpret a box-and-whisker plot, you need to look at three things: the median, the interquartile range, and the outliers. The median is represented by the line in the middle of the box. The interquartile range is represented by the width of the box. The outliers are represented by dots outside of the whiskers.

To find the median, first find the middle value of the data set. If there is an even number of values, then take the mean of the two middle values. To find the interquartile range, subtract the first quartile from the third quartile. To find outliers, look for values that are more than 1.5 times the interquartile range away from either end of the data set.

## Examples of box-and-whisker plots

There are many different types of data that can be represented using a box-and-whisker plot. Here are some examples:

1. A set of data that includes outliers. In this case, the whiskers extend to the furthest data point that is not considered an outlier.

2. A set of data that is skewed to one side or the other. In this case, the median is not in the center of the box, and one of the tails is longer than the other.

3. A set of data with multiple modes (i.e., more than one peak in the distribution). In this case, there will be multiple boxes or whiskers, each representing a mode.

## Conclusion

We hope that this article has helped you understand how to draw a box-and-whisker plot for data. By following these steps, you can easily create visuals of your data and use them to analyze it in meaningful ways. It is essential for business owners, researchers, and others who need to make sense of their data quickly and easily to have a tool like the box-and whisker plot at their disposal. With practice, you will be able to accurately represent data using a box-and-whisker plot with ease.

2. Drawing a box-and-whisker plot for a set of data can help us quickly visualize the data and identify features such as central tendency and dispersion.

Let’s take a look at the data set given here: 21 29 25 20 36 28 32 35 28 30 29 25 21 35 26 35 20 19

This set of data has the following features:

• Range: 19 to 36
• Median: 28
• Quartiles: Q1 = 20, Q3 = 32
• Interquartile Range (IQR): 12

Now, let’s draw the box-and-whisker plot for this data set!

The box-and-whisker plot for the data set is shown below:

As can be seen from the box-and-whisker plot, the median (Q2) is 28. The lower quartile (Q1) is 20 and the upper quartile (Q3) is 32. The interquartile range (IQR) is 12.

The box-and-whisker plot also shows us the range of the data set, which is 19 to 36. The minimum value is 19 and the maximum value is 36.

In conclusion, the box-and-whisker plot allows us to quickly visualize the data and identify features such as central tendency and dispersion. It is an effective tool to quickly summarize a data set and helps us draw conclusions about the data.