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

Lesson 2: Box and whisker plots

# Worked example: Creating a box plot (even number of data points)

Box-and-whiskers plots help visualize data ranges and medians. First, arrange your numbers from least to greatest. The smallest and largest numbers form the 'whiskers'. The median of the entire data set splits the 'box' in the middle. The medians of the top and bottom halves of the numbers form the 'box' boundaries.

## Want to join the conversation?

• can i get some help what does IQR mean
• The interquartile range. Where you subtract Quartile 3 and Quartile 1.
• Shouldn't the upper quartile be 7.5, the average of 7 and 8? Considering the upper quartile consists of six numbers?
• it has 7:5 5 6 7 8 8 10
the first five stays since it is not the median
• The question says to exclude the median when calculating the quartiles. In this video they have included median.
Can you explain what does exclude means here ?
what I think is, Q3 will be 7.5 and Q1 will be 2.
• When the question states to "exclude the median when computing the quartiles," it means that when you're finding the first quartile (Q1) and the third quartile (Q3), you should not include the median value in the calculations. In other words, the median is not considered when determining the quartiles. Your interpretation is correct: Q1 will be the median of the lower half of the data, and Q3 will be the median of the upper half of the data. So, if the median is 4.5, then Q1 will be the median of the numbers less than 4.5, and Q3 will be the median of the numbers greater than 4.5.

To summarize:

Q1 is the median of the lower half of the data (excluding the median).
Q3 is the median of the upper half of the data (excluding the median).
Based on your calculation, if the median is 4.5, then Q1 could indeed be 2 and Q3 could be 7.5. However, these values might vary depending on the specific distribution of the data points. If you'd like, I can guide you through the process of finding Q1 and Q3 using the given data set.
• I'm confused. In the last worked example when we had an odd number of data, we were taught to eliminate the mean when calculating the upper and lower means. Does that rule not apply with even numbers of data? That was not clear.
• We want the median to divide the data set into two equal halves.
However, with an odd number of data points the two halves can't be equal in size which is why we remove the median before we calculate the upper and lower quartiles.
With an even number of data points we don't have this problem and don't have to remove the median.
• sleep ideas or can you give me some
• Bro dis hard
• Good luck
P.S Just trying to help
• im abt to fall asleep listening to this ngl
• On the previous video, we are told to exclude the median when computing the quartiles, so Sal does. On this video Sal includes them when it says to exclude them. I'm confused!
• How does outliers affect mean
• Outliers tend to skew the mean to the left or right of the center (according to where the outlier is).
For example take this data set {2,6,6,8,9,11} the mean is (2+6+6+8+9+11)/6 = 42/6 = "7"
If we replaced the 11 in our data set with an outlier "41" the new data set becomes {2,6,6,8,9,41} and the new mean becomes (2+6+6+8+9+41)/6 = 72/6 = "12"
Notice that our new mean "12" is outside our original data set, so what that outlier "41" did is it skewed the mean to the right.
On a side note: This effect of outliers does not happen in median (or it does not change that much); notice that the median is the arithmetic mean of 6 and 8, i.e, the median is 7 in both data sets.
(1 vote)
• I dont know how to create a box plot from a histogram. Help please!