In this lessons, we will certainly learn exactly how to construct and read a box plot (also recognized as box-and-whisker plot).

You are watching: How to find the upper extreme

Related PagesGraphical approaches For explicate DataBar ChartsCumulative Frequency TableStatistics Lessons

A crate plot (also called a box and whisker plot) reflects data using the center value the the data and also the quartiles, or 25% departments of the data.

The adhering to diagram shows a crate plot or box and whisker plot. Scroll under the web page for more examples and solutions using box plots.


Drawing A Box and also Whisker Plot

Example:Construct a crate plot because that the complying with data:12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25

Solution:Step 1: species the data in ascending order.

Step 2: find the median, reduced quartile and also upper quartile.


Median (middle value) = 22 reduced quartile (middle worth of the lower half) = 12 upper quartile (middle worth of the top half) = 36

(If over there is an even number of data items, then we require to gain the typical of the center numbers.)

Step 3: attract a number line the will encompass the smallest and also the largest data.


Step 4: attract three upright lines in ~ the reduced quartile (12), typical (22) and the upper quartile (36), just over the number line.


Step 5: join the lines for the reduced quartile and the top quartile to kind a box.


Step 6: draw a heat from the smallest worth (5) to the left next of the box and also draw a heat from the ideal side of package to the greatest value (53).


How To draw A Box and also Whiskers Plot for A set Of Data?

Example:Make a box-and-whisker plot because that the adhering to data set.7, 3, 14, 9, 7, 8, 12.

How to analyze a box and also whisker plot?

Box and Whisker Plots room graphs that show the distribution of data follow me a number line. We can construct crate plots by bespeak a data collection to find the average of the collection of data, mean of the upper and lower quartiles, and upper and lower extremes. We can draw a Box and Whisker plot and also use crate plots to solve a real world problem. By recognize the center values the the notified data set, you have actually separated the data into four equal groups dubbed quartiles. A shorter distance method the quartile data is bunched together. A longer distance means the quartile data is spread out.

For example, if your job is to compare the yearly snowfall between two ski resorts because that the previous 50 years, you would require a method to summarize all the data. A box plot displays the range and circulation of data follow me a number line.

How To do A crate Plot indigenous A set Of Data?

Order the data from the very least to greatest.Find the mean or center value that splits the collection of data into two same groups. If over there is no one middle value, use the typical of the two center values together the median.Find the mean for the lower half of the data set.Find the average for the upper half of the data set.Use these 5 values to construct a box plot: lower extreme, lower quartile, median, top quartile, top extreme.Plot the points of the 5 values above a number line.Draw upright lines with the lower quartile, median and upper quartile.Form a box by connecting the upright lines indigenous the reduced quartile, median, and upper quartile.Draw the whiskers from the extremes come the box.

Outliers In A Box and Whiskers Plot

What is an outlier?An outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which the occurs.

Inter-Quartile variety (IQR) is the distance in between the first and second quartiles.Multiply the IQR by 1.5.Subtract that worth from the first Quartile to gain your lower boundary.Add that worth to the 2nd Quartile to get your upper boundary.Values in the data collection that fall exterior of these boundaries are taken into consideration outliers.

Understanding & compare Boxplots (Box and Whisker Plots)

Box and whisker plots space graphical display screens of the 5 number review (minimum, quartile 1, median, quartile 3, and also maximum).

Compare 2 boxplots and see exactly how larger spread renders predictions more difficult.

See more: How Much Cheese To Make 1 Cup Shredded, Cheese Block

Check for evidence of claim using the boxplots.

Try the cost-free Mathway calculator and also problem solver below to practice miscellaneous math topics. Shot the given examples, or form in your very own problem and also check her answer through the step-by-step explanations.