**Box and whisker plot :**

Box and whisker-plot is the graph used in statistics to represent the central 50% of the values of a data set.

The picture figure given below clearly illustrates this.

In the above figure, the box spans interquartile range (central 50%).

To draw box and whisker-plot graph for a data set, we have to know lower quartile, upper quartile and median.

To construct box and whisker-plot for the given data set, we have to do the following steps.

Step 1 :

Write the observations of the given data set in ascending order.

Step 2 :

Find lower quartile, upper quartile and median using the formulas given below.

Lower quartile = (n+1)/4

Upper quartile = 3(n+1)/4

Median = (n+1)/2

Here, n = number of observations in the given data set.

Step 3 :

Using lower quartile, upper quartile and median, we have to construct box and whisker-plot as given in the above picture.

Construct box and whisker-plot for the data given below.

4.3, 5.1, 3.9, 4.5, 4.4, 4.9, 5.0, 4.7, 4.1, 4.6, 4.4, 4.3, 4.8, 4.4, 4.2, 4.5, 4.4

**Construction of box and whisker-plot :**

**Step 1 : **

Let us write the observations in the data in ascending order.

3.9, 4.1, 4.2, 4.3, 4.3, 4.4, 4.4, 4.4, 4.4, 4.5, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0, 5.1

**Step 2 : **

Number of observations (n) = 17

Let us find lower quartile, upper quartile and median.

**Lower quartile : **

Lower quartile = (n+1)/4 = (17+1)/4 = 18/4 = 4.5

Lower quartile comes in between 4th and 5th observations.

So, lower quartile = average of 4th and 5th observations

Lower quartile = (4.3 + 4.3)/2 = 8.6/2 = 4.3

**Upper quartile : **

Upper quartile = 3(n+1)/4 = 3(17+1)/4 = 54/4 = 13.5

Upper quartile comes in between 13th and 14th observations.

So, upper quartile = average of 13th and 14th observations

Upper quartile = (4.7 + 4.8)/2 = 9.5/2 = 4.75

**Median : **

Median = (n+1)/2 = (17+1)/2 = 18/2 = 9

Median is exactly the 9th observation.

So, median = 4.4

**Step 3 : **

Using lower quartile, upper quartile and median, we can construct box and whisker-plot graph as given below.

After having gone through the stuff given above, we hope that the students would have understood "Box and whisker-plot".

Apart from the stuff given above, if you want to know more about "Box and whisker-plot",please click here

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**