@@@@@@@@@@@Pie Charts and Standard Deviation.pptx@@@@@@@@@
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Transcript of @@@@@@@@@@@Pie Charts and Standard Deviation.pptx@@@@@@@@@
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.
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
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 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