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 basic mathematics image

Box and whiskers plot


Before studying this lesson, you need to understand the median. Basically a box and whiskers plot looks like this:

box-and-whiskers-image



Just like the name suggests, the rectangle you see is called a box. And the reason we call the two lines extending from the edge of the box whiskers is simply because they look like whiskers or mustache, especially mustache of a cat

The five points or dot that you see represents the followings starting from left to right

box-and-whiskers-image


Lower extreme: the lowest or smallest value in a set of data

Lower quartile or first quartile: the median of all data below the median

Median or second quartile: the middle value of the set of data. If there are two values in the middle, the median is the average of the two values

Upper quartile or third quartile: the median of all data above the median

Upper extreme: The biggest value in the set

Example:

Construct a box and whiskers plot for the data set: {5, 2, 16, 9, 13, 7, 10}

First, you have to put the data set in order from greatest to least or from least to greatest

From least to greatest we get : 2    5    7    9    10     13    16

Since the smallest value in the set is 2, the lower extreme is 2

Since the greatest value in the set is 16, the upper extreme is 16

Now, look carefully at the set:  2    5    7    9    10     13    16

You can see that 9 is located right in the middle of the set of data

Therefore, 9 is the median

Now to get the lower quartile, you need all data before the median or 9

2    5    7    9    10     13    16

In bold right above we show all data before 9, so  2    5    7   

Since the value in the middle for the set   2    5    7    is 5, the lower quartile is 5

Finally, to get the upper quartile, you need all data after the median or 9

2    5    7    9    10     13    16

In bold right above we show all data after 9, so  10    13    16   

Since the value in the middle for the set   10    13    16    is 13, the upper quartile is 13

Now make a number line and graph above the number line 2, 5, 9, 13, and 16 with five dots: one dot will represent the median, one dot will represent each extreme, finally, one dot will represent each quartile.

Your graph should look like this after you are done

number-line-and-dots-image



Draw a rectangle or box starting from the lower quartile to the upper quartile. Draw a vertical segment too to represent the median

box-image



Finally, draw horizontal segments or whiskers that connect all five dots together.

The box and whiskers plot for {5, 2, 16, 9, 13, 7, 10} is :

box-and-whiskers-image










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