THE BOX AND WHISKERS

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.

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 two values.

Upper extreme: the biggest value in the set.

Example 1:

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

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

Red color number 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 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

your graph should look like this

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

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 :

 Example 2: 

Questions that you can try:

1.

2.

 

3. 

GOODLUCK!😊😊😊