MATH 1040 - EXAM 1
What is data?
Consist of info coming from observations, counts, measurements or responses
T/F: Nominal levels of measurement use math computations
FALSE - none
T/F: Interval data has an inherent zero
FALSE - ratio does
The graph to the right shows the responses to the question, "Does global warming contribute to El Nino?" Identify the level of measurement of the data listed on the horizontal and vertical axes in the figure. Horizontal: Response (very likely --> unsure) Vertical: Percent
Horizontal: ordinal Vertical: Ratio
What level of measurement can be ordered and differences between data entries are meaningful, but a zero entry is *not* an inherent zero?
Interval
What is the difference between class limits and class boundaries?
Class limits are the least and greatest numbers that can belong to the class. Class boundaries are the numbers that separate classes without forming gaps between them. For integer data, the corresponding class limits and class boundaries differ by 0.5.
What level of measurement is used for names, labels, qualities and has no math computations?
Nominal
Which level of measurement can have no mathematical computations?
Nominal
The list of books that your friend read for school for the past 5 months is shown below. Gone Girl Private London Spring Fever Threat Vector What is the data set's level of measurement? Explain your reasoning.
Nominal - data are categorized using names, labels, or qualities, but the data
The jersey numbers for players on a baseball team are listed below 10 7 40 13 9 12 15 What is the data set's level of measurement? Explain your reasoning.
Nominal. - data are categorized using numbers, but no mathematical computation can be made
What is the level of measurement for "happiness level (scale of 0 to 10)"?
Ordinal
Which level of measurement can be arranged in order, or ranked, but differences between data entries are not meaningful?
Ordinal
The regions with the 6 highest volumes of sales for a corporation last year are shown below. 1. west 2. ne 3. east 4. n 5. s 6. se What is the data set's level of measurment?
Ordinal - ranked or ordered in some manner (the sales can be ranked by the highest volumes but it is qualitative data)
What level of measurement is change in health (scale of -5 to 5) considered?
QUALITATIVE --> ordinal
Major, eye color and place of birth are all describing what type of data?
Qualitative
The regions with the 6 highest volumes of sales for a corporation last year are shown below. 1. west 2. ne 3. east 4. n 5. s 6. se Are the data qualitative or quantitative?
Qualitative
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Colors of automobiles
Qualitative - attribute or labels
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Gender of students in a class
Qualitative - attributes or labels
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Amount of disk space in gigabytes
Quantitative - amount of disk space is found by measuring or counting
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Weight
Quantitative - found by measuring or counting
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Times to complete an obstacle course
Quantitative - numerical measurement
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Times to run 100 meters
Quantitative - numerical measurements
The masses (in grams) of a sample of a species of a fish caught int he waters of a region are shown below: 22.7 23.8 23.9 23.4 20.3 19.3 Determine the level of measurement of the data set? Explain your reasoning.
Ratio - data can be ordered and differences between data entries are meaningful, and a zero entry is an inherent zero
Determine whether the variable is qualitative or quantitative. Explain your reasoning. Favorite color
The variable is qualitative - color describes an attribute or characteristic
What is the difference between a random sample and a simple random sample?
With a random sample, each individual has the same chance of being selected. With a simple random sample, all samples of the same size have the same chance of being selected.
What is qualitative data?
consists of attributes, labels, or non-numerical entries (categorical)
What type of statistics consists of tables, charts, averages etc?
descriptive
What are the branches of statistics?
descriptive and inferential
What is the level of measurment for "marital status"?
nominal
What level of measurement are allergies listed on a medical form considered?
nominal
What levels of measurement can be qualitative?
nominal ordinal
What are the different levels of measurement?
nominal, ordinal, interval, ratio
What is a parameter?
numerical description of a population
What is a statistic?
numerical description of a sample
What is quantitative data?
numerical measurements or count
What level of measurement can rank or order the data in some manner, without having meaningful differences between the data entries?
ordinal
Which level of measurement can be qualitative or quantitative?
ordinal
What are some benefits of representing data sets using frequency distributions?
organizing the data into a frequency distribution can make patterns within the data more evident
What is the numerical description of a population?
parameter
What level of measurement is height considered?
quantitative --> ratio
What is the level of measurement for "height"?
ratio
Which level of measurement has a true (inherent) zero?
ratio
What is the ratio level of measurement?
ratio of 2 data values can be formed zero entry is an inherent zero (implies "none") e.g. height (can say someone is twice as tall as somebody else)
What is the numerical description of a sample?
statistic
What is a population?
the collection of *all* outcomes, responses, measurements or counts that are of interest
What are the experimental units
the individuals on which the experiment is done
What is statistics?
the science of collecting, organizing, analyzing, and interpreting data in order to make decisions
What are inferential statistics
using sample data to draw conclusions about a population
What type of zero does interval level of measurement have?
zero represents a position on a scale (not an inherent zero; place holder) e.g. year of birth --> the year 0 exists
Is this an example of descriptive or inferential statisics? Population: all male students (parameter) - average height Sample: 50 random selected students (statistic) - average ht from sample
Descriptive
T/F: Interval data can be ordered
TRUE
A Pharmaceutical company wants to test the effectiveness of a new allergy drug. The company identifies 250 females 30-35 years old who suffer from severe allergies. The subjects are randomly assigned into two groups. One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug. After six months, the subjects' symptoms are studied and compared. Identify a potential problem with the experiment design being used and suggest a way to improve it.
There may be a bias on the part of the researcher if the researcher knows which patients were given the real drug.
What is a sample?
a subset, or part of, the population e.g. population: all responses of US employees; sample: 834 surveyed "responses"
What is an inherent zero?
a zero that implies none -ratio
`A pharmaceutical company wants to test the effectiveness of a new allergy drug. The company identifies 250 females 30-35 years old who suffer from severe allergies. The subjects are randomly assigned into two groups. One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug. After six months, the subjects' symptoms are studied and compared. What is the: experimental unit? treatment?
experimental unit: 30-35 years old who suffer from severe allergies treatment: new allergy drug
Select 3 examples of data sets that do not have inherent zeros below. Temperature in degrees F Average IQ score of a high school class Average monthly precipitation in inches Average age of college students in years Maximum wind speed during a hurricane A student's level of happiness measured from 0 to 10
i.e. the zero represents a position on a scale, place holder -Temperature in degrees F -Average IQ score of a high school class -A student's level of happiness measured from 0 to 10
What type of statistic draws a conclusion?
inferential
Select 3 examples of data sets that have inherent zeros below: Temperature in degrees F Average IQ score of a high school class Average monthly precipitation in inches Average age of college students in years Maximum wind speed during a hurricane A student's level of happiness measured from 0 to 10
inherent = 0 implies none -Average monthly precipitation in inches -Maximum wind speed during a hurricane -Average age of college students in years
What is the level of measurement for "year of birth?"
interval
What level of measurement is year of birth considered?
interval
What levels of measurement can be quantitative?
interval ratio sometimes ordinal
What is the difference between ordinal and interval data?
interval has data that has differences in the data entries that is meaningful e.g. year of birth
What are descriptive statistics?
involves organizing, summarizing and displaying data e.g. tables, charts, averages