# The Student Success Commons at York County Community College: MAT 118: Quantitative Reasoning

## Chapter 3D

### Mini Math Tutoring Videos:

#### UNITS

##### • You can cancel units that appear in the top and bottom of one fraction, or in the top of one fraction and in the bottom of another as long as the two fractions are being multiplied (see the Unit analysis (cancelling units) PDF)

 KEY WORD MATHEMATICAL MEANING EXAMPLE per division "miles per hour" can be written mathematically as "miles ÷ hours" or "mi/hr" of multiplication "50% of 10" can be written mathematically as "0.50 × 10" (Note: in almost all cases, percentages must be written as their decimal equivalents. To convert a percent to a decimal you must divide the percent by 100 and drop the % symbol.) is equals "The price is \$30" can be written mathematically as "price = \$30" what an unknown value (a variable), usually represented by a letter like x "What is 50% of 10" can be written mathematically as "x = 0.50 × 10"

## Chapter 6A

### Mini Math Tutoring Videos:

#### SAMPLE VS. POPULATION

POPULATION: The population is the complete set of people or things being studied.

SAMPLE: The sample is a subset of the population. The population is usually too large to look at in its entirety, so a sample that represents the population must be chosen and data can be gathered from the sample.

SAMPLE STATISTICS: Sample statistics are numbers describing characteristics of the sample. This data is gathered directly from the sample.

POPULATION PARAMETERS: Population parameters are specific numbers of interest that describe certain characteristics of the population. The population parameter is usually based on the sample statistic.

For example:

A YCCC student wants to know how many U.S. community college students have pets. She gathers information from 698 community college students and found that 422 of them have pets.

In this example:

• the population is all U.S. community college students.
• the sample is the 698 U.S. community college students that were surveyed.
• the sample statistic is the 422 out of 698 U.S. community college students who have pets, which is about 60.5%.
• the population parameter is the number of all U.S. community college students who have pets. Note that it is not expressly stated, but if the statistical study was performed properly, we can estimate that about 60.5% of all U.S. community college students have pets.

#### SAMPLING METHODS

##### NOTES AND EXAMPLES
Simple random This is when the sample is chosen in such a way that every sample of the same size has an equal chance of being selected.

Examples:

• Names are put in a hat and randomly picked.
• Every item in the population is assigned a number and numbers are randomly chosen by a computer program
Systematic This is when the sample is chosen according to some kind of mathematical pattern.

Example:

• Every 10th person on the list is surveyed.
Convenience This is when a sample is chosen because it is convenient.

Examples:

• Every person who comes out of the post office is surveyed.
• People watching a certain television show are asked to call in to cast their vote.
• People are asked to mail in their response to a survey in a magazine.

Note: This type of sampling can often lead to bias.

Stratified

For this sampling method we must first define different subgroups, called strata, within the population, then we must select a sample from each of the subgroups.

Researchers use stratified sampling to ensure specific subgroups are present in their sample

Examples:

• The population of a town is broken down into different age groups, and 30 people are chosen from each of the different age groups
• The plants in a nursery are separated into groups based on the amount of sun they require.

## Chapter 10A

### Student Success Commons at York County Community College

##### 112 College Drive Wells, ME 04090studentsuccesscommons@yccc.edu 207-216-4386

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