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# Interpreting box plots

A box and whisker plot is a handy tool to understand the age distribution of students at a party. It helps us identify the minimum, maximum, median, and quartiles of the data. However, it doesn't provide specific details like the exact number of students at certain ages.

## Want to join the conversation?

• quartile: The values that divide a list of numbers into quarters.
• i am very confused where did he get precents from
• Think of the box-and-whisker plot as split into four parts (the first, second, third, and fourth quartiles), making each part equal to 1/4 (essentially 25%) of the plot.

As shown in the video, there are three quartiles that have values larger than ten; that means that 3/4 of the quartiles have kids older than 10. In other words, 75% of the plot accounts for kids 10 and older (since 3/4 can be written as 75%).

The fact that every quartile is 25% is a guestimate; the point is that all three quartiles should add up to at least 75% of the plot.

Hope this clears things up!😄
• At , Isn't there 50% on one side of the median and 50% on the other so technically isn't 13 still in the middle so therefore it would be true? Thanks!
• the sign with the curly = sign means that it is approximated, so he can't be sure that it is truly 50% on that side, on the flip side, because we don't know, it might as well be like that.
• At , when he says that it is the second quartile, wouldn't that be Q1 and the median be Q2?
• No, this is because the first quartile is the line before the box.
• I do not get the last statement. We DO know that exactly half of the students are older than 13, because 50% is on the right side of the median which is also 13. Don't we?
• If he'd said that exactly 50% ARE 13 or older, that would be true, because it includes the median.

For example, if i say that 5 is greater than 10/2, that would be false. Because 10/2 is 5, but i said it was GREATER. On the other hand, if i said that 5 >= 10/2 (greater or equal to), that would be true.
• Would it be true if the second question was "Exactly 75% of the students are >10"?
• No.

As an example, let's say there were 17 students at the party, of the following ages:
7, 8, 8, 9, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16

The median is 13.
The second quartile is 10.
The third quartile is 15.
The minimum age is 7.
The maximum age is 16.
So, this data set gives the same box plot as shown in the video.

But 13 of the 17 students are older than 10.
13∕17 ≈ 76.47%, which is of course greater than 75%.

So, the number of students older than 10 is not necessarily exactly 75%.
• How does he find 25%
• please vote on this comment