# The A to Z of mathematics a basic guide - Sidebotham T.H.

ISBN 0-471-15045-2

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References: Bias, Population, Questionnaire, Random Sample, Sample, Statistics.

CENTER OF ENLARGEMENT 69

CENTER OF A CIRCLE

Two methods of finding the center of a circle are as follows:

1. Paper folding. This is best done if the circle is cut out, but it is not essential. Fold the circle exactly in half and crease the paper (see figure a). Open the circle out and repeat the process, but producing a different fold. The point where the two folds intersect is the center of the circle.

2. Construction using compasses. This method is appropriate if the circle cannot be folded. For a large circle, such as a flowerbed or a lawn, a piece of rope with a stick fastened at each end will serve as an improvised compass.

Choose any two points on the circumference of the circle and call them A and B (see figure b). Open the compasses to any distance, but greater than half the length from A to B. Draw a semicircle with A as the center. Using the same radius, draw a semicircle with B as the center. Draw in the straight line which passes through the two points where the semicircles intersect. This line is called the mediator of the points A and B, and is also called the perpendicular bisector of the line segment AS. Repeat the steps to construct the mediator for another pair of points C and D that lie on the circumference of the circle. The point where the two mediators intersect is the center of the circle.

First fold

Second fold

Center

C Center

\ of circle

(b)

References: Circle, Circumference, Mediator, Perpendicular Bisector, Radius, Semicircle.

CENTER OF ENLARGEMENT

Reference: Enlargement.

70 CENTRAL TENDENCY

CENTER OF ROTATION

Reference: Rotation.

CENTI

A prefix which means one-hundredth part of some quantity. One hundredth written as a fraction is 1/100. For example, one-hundredth part of a meter is called a centimeter, which is abbreviated cm, where c stands for centi and m stands for meter. Metric units are mainly based on dividing (or multiplying) some quantity by 1000, so the prefix centi does not have much use except in centimeter and in cent, which is 1/100 of a dollar.

References: Meter, Metric Units.

CENTIGRADE

Reference: Temperature.

CENTIMETER

References: Centi, Metric Units.

CENTRAL TENDENCY

For a normal distribution that has been ranked in order of size, the three averages mean, mode, and median tend to be near the center of the ranking. We say that they are measures of central tendency for the distribution. The larger the quantity of data, the more likely it is that the three averages will be closer and closer to each other in value and closer to the center. For a small quantity of data that is not normally distributed the three averages are not expected to be near the center of the ranked data.

The study of central tendency offers an opportune time to discuss the three averages mean, mode, and median as representative values. They can be used to represent a quantity of data in order to compare that quantity of data with another. Suppose we are comparing and contrasting the goal-scoring capabilities of two soccer teams, United and Rovers, who are of similar ability. The goals each team has scored in their last 17 games are given in the following table:

United 2392293144301 13 10 0

Rovers 334143052243442 24

CGS SYSTEM OF UNITS

71

In order to analyze the two sets of data, it is useful to rank the scores for each team:

Mode

United 001 1 1 22233334499 10 total = 57

Rovers 0122223333444444 5 total = 50

Write

Medians

The mean for United

Mode

57

17

3.4 (to 1 dp)

50 17

= 2.9 (to 1 dp)

These data, along with the range, are summarized in the following table:

The mean for Rovers

Mean Mode Median Range

United 3.4 3 3 10

Rovers 2.9 4 3 5

The representative values (mean, mode, and median) are useful for comparing two sets of data, provided they truly represent their set. This means that the representative value will stand in place of the whole set of data and accurately reflect the properties of the set. We will compare each of the values mean, mode, and median for United’s and Rovers’ data and see if they represent each team’s goal-scoring abilities.

None of the three values represents United, because they are so inconsistent and the range of 10 goals is so large. On the other hand, the data for Rovers is more closely clustered about the mean and median, which is a sign of their consistency. For Rovers their mean and median would be good representative values, but not the mode.

Conclusion: If the two teams played each other, I would expect Rovers to win, because they consistently, game by game, score more goals than United. In two games United scored high, but they lack consistency. This conclusion does not take into consideration the number of goals scored against either team, since we have no knowledge of this information.

References: Average, Data, Mean, Median of a Set of Data, Mode, Normal Distribution, Range.

CGS SYSTEM OF UNITS

This system of measuring quantities was based upon the metric system and used centimeters (cm) to measure length, grams (g) to measure mass, and seconds (s) to

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