If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Get ready for AP® Statistics>Unit 2

Lesson 3: Comparing data displays

# Comparing dot plots, histograms, and box plots

Data can be represented in various ways such as dot plots, histograms, and box plots. Dot plots and box plots are useful for finding the median, while histograms are great for showing the number of values within a specific range.

## Want to join the conversation?

• Is there anywhere that I can find what a box plot is and how they work? I have never heard of it before, and I do not understand how Sal is reading it throughout the video, or even what it is. Is it simply showing the range of the data points? Or is there more to it? And what does the box in the middle represent? Is there anywhere on Khan Academy that I can find this?
• A box plot (aka box and whisker plot) uses boxes and lines to depict the distributions of one or more groups of numeric data. Box limits indicate the range of the central 50% of the data, with a central line marking the median value. Lines extend from each box to capture the range of the remaining data, with dots placed past the line edges to indicate outliers.
• is there a short cut to finding the median and mode of a group of numbers?
• the mode is the most common number like 1,1,2,2,3,3,3,4,5,5,5,5,5,6,7,8,9,10,11, the mode is 5 I do not know any shortcut to the median
• What the heck is a box plot? I never saw Sal talk about it in the previous videos.
• Box plot is short for Box and whisker plot.
• How are dot plots and bar graphs similar?
• A dot plot is when you have dots represent as certain number of something (usually 1), where you can tell what it is representing by looking at the x-axis and you can tell how much there is by counting the dots. A bar graph is when you have one bar representing a number of something (and usually more than one bar), and you can tell what is representing by looking at the x-axis and you can tell how much there is by looking at y-axis and what number on it corresponds to the top of the graph. So basically, a dot graph is a bar graph with dots instead of bars and no y-axis.
• What in the world is a box plot? This was not covered anywhere in this section? Nor was finding a median! Help!
• The median is really easy to find. It's just the middle number in a set of data. If there are a even number of data, the median is the average of the 2 middle numbers. For example, the median in this set of data:
1 3 5 5 7
Is 5, because 5 is the middle number. In this set:
2 4 6 8
There are two middle numbers, 4 and 6. The median would be the average of the two, which means it's 5. Please note that before you find the middle number, the data must of course be organized from smallest to largest value. So for example,
1 3 7 8 9 3 2
Must be reordered as:
1 2 3 3 7 8 9
To find the median 3.
Now, a box plot is difficult to explain without a visual, so try going here: https://www.khanacademy.org/math/probability/data-distributions-a1/box--whisker-plots-a1/v/reading-box-and-whisker-plots
• What is quartile and interquartile?
• Well, there is an interquartile range. You can summarize the majority of data by using the interquartile range. The interquartile range is a value that is the difference between the upper quartile value and the lower quartile value. In descriptive statistics, the quartiles of a ranked set of data values are the three points that divide the data set into four equal groups, each group comprising a quarter of the data.
• What is the difference between a histogram and a bar graph? They look the same to me!
• A histogram takes the number of how many something are and add them up. Like if you were selling flip flops than on a histogram it would just be the number of flip flops. But on the bar graph you would have how many you sold with the price.
• In the practice questions preceding this video (labelled "Practice: Comparing distributions), you use box and whisker plots and ask questions about the average values of two data sets. I believe that your earlier discussion of box and whisker plots stated that the middle line showed the median, not the average. If this is the case, then it is not possible to use a box and whisker plot to answer questions regarding the average (arithmatic mean) of a data set. In the alternate, if the middle line in a box and whisker plot represents the arithmatic mean of a data set, then you should take care to refer to it as such in earlier videos. At of this video, you state that the middle line of the box plot "explicitly tells us what the median is."
• i am lost after how can you tell which one to use?
• So the first question, "Which display can be used to find how many vehicles had driven more than 200,000 km?" is asking: FROM WHICH GRAPH can you clearly see the EXACT number of vehicles have driven more than 200,000 km? The answer would be the histogram, because you can tally up the number of cars by counting- aka you get an exact number.

The second question, "Which display can be used to find that the median distance was approximately 140,000 km?" is asking: FROM WHICH GRAPH can you see that the median distance (or the MIDDLE VALUE) is approximately 140,000 km? So the answer to that would be the box and whisker plot, because if you know how a box and whisker plot works, you'll know that the line in the middle of the box is the median. In this case, you'll find that the median is approximately 140,000 km.

Hope this helps!