Mathematics meaning of terms page 8

Ordered pair
A special type of set of two elements for which order is significant. For example, the co-ordinates in the Cartesian plane (3,4) represent the point where  and . Grid references used on a map are also examples of an ordered pair.  See: grid reference, Cartesian co-ordinate system.
Outlier
An outlier is a data value that appears to stand out from the other members of the data set by being unusually high or low. The most effective way of identifying outliers in a data set is to graph the data.

For example, in the following list of ages of a group of 10 people,
{ 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 24 }, 24 would be considered to be a possible outlier.

As a rule of thumb, a value which is more than 1.5 interquartile ranges less than the lower quartile, or greater than the upper quartile, is a possible outlier. See also: data, interquartile range (IQR).

P
Parabola
The graph of  is called a parabola. The point  is called the vertex of the parabola and the -axis () is the axis of symmetry of the parabola called simply the axis.

Some other parabolas are the graphs of  where . More generally, every parabola is similar to the graph of .
Parallel
Two lines are parallel if they have no points of intersection in the plane, and the same gradient (slope) in the coordinate plane. The symbol || is often used to mean one ray or line segment is parallel to another. For example, the two lines below are parallel:

For a geometric figure such as the parallelogram shown below, different numbers of arrow heads may be used to denote sets of lines which are parallel. For example, the pair of lines BA and CD are a parallel pair (two arrowheads on each) while AD and BC are another parallel pair (one arrowhead on each). Note that BA is not parallel to AD, for example.

Parallel box-and-whisker plots
Parallel box-and-whisker plots are used to visually compare the five-number summaries of two or more data sets. The term ‘parallel box-and-whisker plot’ is commonly abbreviated to ‘parallel boxplot’.

For example, a parallel box-and-whisker plot below can be used to compare the five-number summaries for the pulse rates of 19 students before and after gentle exercise.

Note that the box plot for pulse rates after exercise shows the pulse rate of 146 as a possible outlier. This is because the distance of this data point above the upper is more than 1.5 times the interquartile range. See also: interquartile range, outlier.
Parallelogram          
A parallelogram is a quadrilateral whose opposite sides are parallel. The quadrilateral ABCD shown below is a parallelogram because BA || CD and AD || BC.

Properties of a parallelogram

• The opposite angles of a parallelogram are equal.
• The opposite sides of a parallelogram are equal.
• The diagonals of a parallelogram bisect each other.

See also: parallel.

Partition
To partition is to divide into separate parts which together constitute the whole. For example, the letters of the alphabet can be partitioned into vowels and consonants, the set of natural numbers can be partitioned into those with remainder 0, 1 or 2 on division by 3.

In the early years it commonly refers to the ability to think about numbers as made up of two parts, for example, 10 is 8 and 2. In later years it refers to dividing both continuous and discrete quantities into equal parts.
Percentage
A percentage is a ratio to 100 or a fraction whose denominator is 100. For example,  percent (written as ) is the percentage whose value is .

Similarly, 40 as a percentage of 250 is .
Percentile
The percentile is the value which corresponds to a cumulative frequency of   for a sample size.

The first quartile () is the 25th percentile, the second quartile (the median or ) is the 50th percentile, and the third quartile () is the 75th percentile. The maximum value of a data set is the 100th percentile (all other values are less than this).

For example, for a sample of 4 students (), the students heights in cm are found to be 150, 152, 156 and 167. The median value of 154 is the 50th percentile as 50% of the data values (2 values) are smaller than this since   (.
See also: interquartile range.
Perfect square
A number is a perfect square if it is the square of an integer or rational number. For example, 169 is a perfect square as 132 = 169. Similarly, 0.81 is a perfect square since
(9/10)2 = 0.81. Perfect squares can also be represented pictorially; for example, the perfect squares 1, 4, 9 and 16 could be shown using the arrays:

See also: array, square number.
Perimeter
The perimeter of a plane figure is the length of its boundary.
Periodic
Appearing or occurring at regular intervals. The function  is periodic because it has
-intercepts which occur periodically at each integer multiple of .
Perpendicular
Two lines, rays, line segments, vectors, planes or other quantities are considered perpendicular if they intersect at a 90° angle (a right angle).

In the diagram below, the line segments BD and BC are perpendicular, while the line segments AB and BC are parallel.

See also: angle, parallel.

Pi
Pi is the name of the Greek letter , that is used to denote the ratio of the circumference of any circle to its diameter.

The number  is irrational as the digits in the continued decimal expansion of π do not have any recurring pattern. The approximate value of , correct to 2 decimal places is 3.14, and 22/7 is a reasonably accurate fraction approximation to π. The decimal expansion for  to 100 significant figures is:

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068…

There is a very long history of attempts to estimate  accurately. One of the early successes was due to Archimedes (287–212 BC) who showed that . The decimal expansion of  has now been calculated to at least the first  places.

See also: circle, diameter, circumference, irrational number.