Mathematics for Technology I (Math 1131)

Durham College, Mathematics
Free
• 55 lessons
• 1 quizzes
• 10 week duration
• Numerical Computation

Here you'll be introduced to the bare basics of mathematics. Topics include commonly used words and phrases, symbols, and how to follow the order of operations.

• Measurements

An introduction to numerical computation. Emphasis is placed on scientific and engineering notation, the rule of significant figures, and converting between SI and Imperial units.

• Trigonometry with Right Triangles

Here we focus on right angle triangles within quadrant I of an x-y plane. None of the angles we evaluate here are greater than 90°. A unit on trigonometry with oblique triangles is covered later.

• Trigonometry with Oblique Triangles

This unit is a continuation of trigonometry with right triangles except we'll extend our understanding to deal with angles *greater* than 90°. Resolving and combining vectors will be covered at the end of this unit.

• Geometry

This unit focuses on analyzing and understand the characteristics of various shapes, both 2D and 3D.

Mean

The mean is a number that shows the center of the data. Another word for mean is average and it is mathematically symbolized as x̄ (x-bar). However, when calculating the mean of the whole population, you use the Greek letter μ (mu) instead.

To calculate the average of a sample, you sum all the observations, then divide by the number of observations (n). The formula changes slightly for population average. The formulas are below:

Where:

• Σ(x) represents the total sum of the observations.
• n/N represents the number of observations.

Median

The median of a set of numbers arranged in order of magnitude is the middle value of an odd number of measurements, or the mean of the two middle values of an even number of measurements. Median is symbolized as x̃ (x-tilda) or with a capital M.

Question:   Find the median of the following data:   574   635   645   695   736   746   794   894

Solution:   The numbers are in ascending order (always make sure they’re arranged in order of magnitude). There are an even number of observations (n = 8), therefore you take the average value of observation 4 and 5.

$\mathrm{x̃}=\frac{{x}_{4}+{x}_{5}}{2}=\frac{695+736}{2}=715\phantom{\rule{0ex}{0ex}}$

If you’re still confused, two more examples are demonstrated below.

Mode

The mode of a set of numbers is the value(s) that occurs most often in the set.

• The set:   1   3   3   5   6   7   7   7   9   → 7
• The set:   1   1   3   3   5   5   7   7   → 1, 3, 5, and 7
• The set:   1   3   3   3   5   6   7   7   7   9   → and 7

More details on finding the mode can be found in this video.

Mid-range

The mid-range is simply the value midway between the two extreme values, such as the range.

The mid-range for the values   3,   5,   6,   6,   7,   11,   11,   15   is:

Let’s review how to calculate the mean, median, and mode with 2 sample problems.