1.2. An Overview of Data http://www.ck12.org
some randomly assigned treatment(s) on the subjects in an effort to isolate the effect of a single variable.
In order to summarize a set of data, we often look to a single quantity to describe where it is centered. There are
various measures that are used for this summary, including themean,median, andmode. These will be covered
in detail in later sections, but they are generally referred to asmeasures of center. Similarly, for information about
how the data is spread out, we investigatemeasures of spreadthat include therange,interquartile range, and
standard deviation.
Points to Consider
- How do we summarize, display, and compare data measured at different levels?
- What are the differences between an observational study and an experiment?
- What are the advantages/disadvantages of observational studies and experiments?
- How do you determine which measure of center or spread best describes a particular data set?
Review Questions
- In each of the following situations, identify the level(s) at which each of these measurements has been
collected.
(a) Lois surveys her classmates about their eating preferences by asking them to rank a list of foods from
least favorite to most favorite.
(b) Lois collects similar data, but asks each student what is their favorite thing to eat.
(c) In math class, Noam collects data on the Celsius temperature of his cup of coffee over a period of several
minutes.
(d) Noam collects the same data, only this time using degrees Kelvin. - Which of the following statements isnottrue.
(a) All ordinal measurements are also nominal.
(b) All interval measurements are also ordinal.
(c) All ratio measurements are also interval.
(d) Steven’s levels of measurement is the one theory of measurement that all researchers agree on. - Look at Table 3 in Section 1. What is the highest level of measurement that could be correctly applied to the
variable “Population Density”?
(a) Nominal
(b) Ordinal
(c) Interval
(d) Ratio
Note: If you are curious about the “does not apply” in the last row of Table 3, then read on! There is only one
known individual Pinta tortoise, and he lives at the Charles Darwin Research station. He is affectionately known
as Lonesome George. He is probably well over 100 years old and will most likely signal the end of the species, as
attempts to breed have been unsuccessful. Here is a picture of poor George!
- In each of the following situations, identify if it is an observational study or an experiment.
(a) In an attempt to determine if students prefer bottled water to tap water, you set up a table in the cafeteria
at lunchtime and have students sample some of each and ask them which they prefer.