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

UNITS

• The units of a quantity describe what the quantity measures or counts. Units provide crucial context. For example, if you ask a car mechanic how long it will take to have your radiator fixed and they say "5" you need the units to fully understand their meaning. Is it 5 minutes, 5 hours, 5 days, 5 weeks, 5 months? 

• Unit analysis (also called dimensional analysis) is the process of working with units to help solve problems.

• You generally cannot add or subtract numbers with different units, but you can combine different units through multiplication, division, or raising to powers. Always perform all operations on both numbers and their associated 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)

Click the image below to download the notes that accompany our YouTube video "Which is less expensive: keeping an old car or buying a new one?"

Click the image below to download the notes that accompany our YouTube video "How long will it take an amount of money to triple?"

Click the image below to download the notes that accompany our YouTube video IRA calculations

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.

BASIC STEPS IN A STATISTICAL STUDY:

1. State the goal(s) of the study. Determine the population you want to study and what kind of information you want.
2. Make sure a sample is chosen that represents the population.
3. Collect data from the sample and find the sample statistic of interest.
4. Use the sample statistic(s) to infer the population parameter(s).
5. Draw conclusions. Determine what you learned and how it addresses your goals.

MAJOR TYPES OF BIAS

Selection bias occurs whenever the researches select their sample in a way that would tent to make it unrepresentative of the population. For example, if a researchers wants to gather information on all U.S. college students but only chooses males, the sample will not be representative of the whole population.

Participation bias occurs whenever people choose whether to participate. For example, if people must take action to participate in a study rather than being chosen at random, those who feel more strongly about the survey issue are more likely to participate.

COMMON STATISTICAL GRAPHS

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