PIE CHARTS AND STANDARD DEVIATION

Group 3Osscennie gentles

Circle graph/pie chart is a way of summarizing a set of categorical data or displaying the different values of a given variable (e.g., percentage distribution). This type of chart is a circle divided into a series of segments. Each segment represents a particular category. The area of each segment is the same proportion of a circle as the category is of the total data set.

Circle graphs/pie charts usually show the component parts of a whole. Often you will see a segment of the drawing separated from the rest of the pie in order to emphasize an important piece of information.

The circle graph/pie chart above clearly shows that 90% of all students and faculty members at Avenue High School do not want to have a uniform dress code and that only 10% of the school population would like to adopt school uniforms. This point is clearly emphasized by its visual separation from the rest of the pie.

The use of the circle graph/pie chart is quite popular, as the circle provides a visual concept of the whole (100%). Circle graphs/pie charts are also one of the most commonly used charts because they are simple to use. Despite its popularity, circle graphs/pie charts should be used sparingly for two reasons. First, they are best used for displaying statistical information when there are no more than six components only—otherwise, the resulting picture will be too complex to understand. Second, circle graphs/pie charts are not useful when the values of each component are similar because it is difficult to see the differences between slice sizes.

 

A pie chart (also called a Pie Graph or Circle Graph) makes use of sectors in a circle. The angle of a sector is proportional to the frequency of the data.

The formula to determine the angle of a sector is:

Constructing circle graphsStudy the following steps in constructing

a circle graph:Step 1: Calculate the angle of each

sector, using the formula

Step 2: Draw a circle using a pair of compasses

Step 3: Use a protractor to draw the angle for each sector.

Step 4: Label the circle graph and all its sectors.

EXAMPLE

In a school, there are 750 students in year1, 420 students in year2 and 630 students in year3. Draw a circle graph to represent the numbers of students in these groups.

Solution:Total number of students = 750+ 420+

630+ = 1800

Draw the circle, measure in each sector. Label each sector and the pie chart.

Using circle graphs

We could also use a given circle graph to answer some questions about the data.

EXAMPLE:The following pie chart shows a survey of

the numbers of cars, buses and motorcycles that passes a particular junction. There were 150 buses in the survey.

A) What fraction of the vehicles were motorcycles?

B) What percentage of vehicles passing by the junction were cars?

C) Calculate the total number of vehicles in the survey.

D) How many cars were in the survey?

Solution:A) Fraction of motorcycles

b) To convert the angle of a sector into a percentage, we use the formula:

Percentage

Percentage of cars

c) Let x be the total number of vehicles

The total number of vehicles is 1,800d) Number of cars

Standard deviation

The Standard Deviation is a measure of how spread out numbers are.

Its symbol is σ (the Greek letter sigma)The formula of deviance is the square root of the

Variance. So now you ask, "What is the Variance?"The Variance is defined as: The average of the squared differences from the

Mean.To calculate the variance follow these steps:Work out the mean (the simple average of the

numbers)Then for each number: subtract the Mean and

square the result (the squared difference).Then work out the average of those squared

differences

The Standard Deviation Formula

ExampleYou and your friends have just measured the

heights of your dogs (in millimeters):

The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.

 Your first step is to find the Mean:Answer:Mean = 600 + 470 + 170 + 430 + 300= 19701970÷5= 394

so the mean (average) height is 394 mm. Let's plot this on the chart:

Now, we calculate each dogs difference from the Mean:

To calculate the Variance, take each difference, square it, and then average the result:

So, the Variance is 21,704.

And the Standard Deviation is just the square root of Variance, so:

Standard Deviation: σ = √21,704 = 147.32... = 147 (to the nearest mm)