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what are the three quartiles of 12 10 11 7 9 10 5

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There are THREE quartiles. Start with the second quartile, Q2, also known as the median. It divides the data in half. To find it, put the data in order.

12 10 11 7 9 10 5

becomes

5, 7, 9, 10, 10, 11, 12

The number which falls in the middle of the list is the median. In this case the median is 10. (For data sets with an odd number of entries, the median is always one of the data points. For an even number, you take the average of the two middle-most data points. Here we have an odd number.)

Q2 = medain = 10.

Now, for Q1 and Q3, the other quartiles, do the same thing on the lower and upper halves of the data set. For Q1:

5, 7, 9, 10


Q1 is the average of the two points in the middle: (7+9)/2 = 8 = Q1.

For Q2:

10, 10, 11, 12

Q2 = (10+11)/2 = 10.5

So your THREE quartiles are 8, 10, and 10.5.

 

First off, there aren't just three quartiles.  The word quartiles starts with the prefix quart- which tells us that there should be four of something.  Just like there are four quarts in a gallon.

Here is an example:

The first thing we have to do is organize the numbers in sequential order:

14 16 17 18 21 25 28 32 33 34 37

Next we have to find the median.  Since we have 11 numbers, the median is the fifth number, 25.

Now we have to divide it into quarters, so we must find the medians of the two halves we just created, these are known as the sub-medians.  They will be 17 and 33.

So these numbers are three of the quartiles.  The final one is the largest number.  They get labeled as Q1, Q2, Q3, and Q4.  In your problem these are as follows:

Q1 = 17
Q2 = 25
Q3 = 33
Q4 = 37

Now to draw the box-and-whisker, you draw a number line and above it, draw a line at each of the quartiles and the lowest number in your data.  Then connect the tops and bottoms of the lines for each of the first three quartiles to create the box.  The whiskers are created by drawing lines frome the middle of the outsides of the box, to the middle of the lines.

Sorry I can't show the drawing part, they don't have equation editor abilities on here.  Hope this helps!